Blocks of monodromy groups in complex dynamics
Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than t...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Jones, Rafe [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2010 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© The Author(s) 2010 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Geometriae dedicata - Springer Netherlands, 1972, 150(2010), 1 vom: 27. Mai, Seite 137-150 |
|---|---|
| Übergeordnetes Werk: |
volume:150 ; year:2010 ; number:1 ; day:27 ; month:05 ; pages:137-150 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10711-010-9499-2 |
|---|
| Katalog-ID: |
OLC2039058923 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2039058923 | ||
| 003 | DE-627 | ||
| 005 | 20230503063537.0 | ||
| 007 | tu | ||
| 008 | 200819s2010 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s10711-010-9499-2 |2 doi | |
| 035 | |a (DE-627)OLC2039058923 | ||
| 035 | |a (DE-He213)s10711-010-9499-2-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |q VZ |
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Jones, Rafe |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Blocks of monodromy groups in complex dynamics |
| 264 | 1 | |c 2010 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © The Author(s) 2010 | ||
| 520 | |a Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. | ||
| 650 | 4 | |a Iterated monodromy groups | |
| 650 | 4 | |a Complex dynamics | |
| 650 | 4 | |a Polynomial iteration | |
| 650 | 4 | |a Post-critically finite polynomials | |
| 650 | 4 | |a Conservative polynomials | |
| 650 | 4 | |a Constant weighted sum of iterates | |
| 700 | 1 | |a Peters, Han |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Geometriae dedicata |d Springer Netherlands, 1972 |g 150(2010), 1 vom: 27. Mai, Seite 137-150 |w (DE-627)129385301 |w (DE-600)183909-3 |w (DE-576)014772213 |x 0046-5755 |7 nnns |
| 773 | 1 | 8 | |g volume:150 |g year:2010 |g number:1 |g day:27 |g month:05 |g pages:137-150 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s10711-010-9499-2 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_24 | ||
| 912 | |a GBV_ILN_30 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_2002 | ||
| 912 | |a GBV_ILN_2004 | ||
| 912 | |a GBV_ILN_2006 | ||
| 912 | |a GBV_ILN_2015 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_4116 | ||
| 912 | |a GBV_ILN_4126 | ||
| 951 | |a AR | ||
| 952 | |d 150 |j 2010 |e 1 |b 27 |c 05 |h 137-150 | ||
| author_variant |
r j rj h p hp |
|---|---|
| matchkey_str |
article:00465755:2010----::lcsfoormgopicml |
| hierarchy_sort_str |
2010 |
| publishDate |
2010 |
| allfields |
10.1007/s10711-010-9499-2 doi (DE-627)OLC2039058923 (DE-He213)s10711-010-9499-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jones, Rafe verfasserin aut Blocks of monodromy groups in complex dynamics 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2010 Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates Peters, Han aut Enthalten in Geometriae dedicata Springer Netherlands, 1972 150(2010), 1 vom: 27. Mai, Seite 137-150 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:150 year:2010 number:1 day:27 month:05 pages:137-150 https://doi.org/10.1007/s10711-010-9499-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 AR 150 2010 1 27 05 137-150 |
| spelling |
10.1007/s10711-010-9499-2 doi (DE-627)OLC2039058923 (DE-He213)s10711-010-9499-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jones, Rafe verfasserin aut Blocks of monodromy groups in complex dynamics 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2010 Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates Peters, Han aut Enthalten in Geometriae dedicata Springer Netherlands, 1972 150(2010), 1 vom: 27. Mai, Seite 137-150 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:150 year:2010 number:1 day:27 month:05 pages:137-150 https://doi.org/10.1007/s10711-010-9499-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 AR 150 2010 1 27 05 137-150 |
| allfields_unstemmed |
10.1007/s10711-010-9499-2 doi (DE-627)OLC2039058923 (DE-He213)s10711-010-9499-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jones, Rafe verfasserin aut Blocks of monodromy groups in complex dynamics 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2010 Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates Peters, Han aut Enthalten in Geometriae dedicata Springer Netherlands, 1972 150(2010), 1 vom: 27. Mai, Seite 137-150 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:150 year:2010 number:1 day:27 month:05 pages:137-150 https://doi.org/10.1007/s10711-010-9499-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 AR 150 2010 1 27 05 137-150 |
| allfieldsGer |
10.1007/s10711-010-9499-2 doi (DE-627)OLC2039058923 (DE-He213)s10711-010-9499-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jones, Rafe verfasserin aut Blocks of monodromy groups in complex dynamics 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2010 Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates Peters, Han aut Enthalten in Geometriae dedicata Springer Netherlands, 1972 150(2010), 1 vom: 27. Mai, Seite 137-150 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:150 year:2010 number:1 day:27 month:05 pages:137-150 https://doi.org/10.1007/s10711-010-9499-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 AR 150 2010 1 27 05 137-150 |
| allfieldsSound |
10.1007/s10711-010-9499-2 doi (DE-627)OLC2039058923 (DE-He213)s10711-010-9499-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Jones, Rafe verfasserin aut Blocks of monodromy groups in complex dynamics 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2010 Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates Peters, Han aut Enthalten in Geometriae dedicata Springer Netherlands, 1972 150(2010), 1 vom: 27. Mai, Seite 137-150 (DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 0046-5755 nnns volume:150 year:2010 number:1 day:27 month:05 pages:137-150 https://doi.org/10.1007/s10711-010-9499-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 AR 150 2010 1 27 05 137-150 |
| language |
English |
| source |
Enthalten in Geometriae dedicata 150(2010), 1 vom: 27. Mai, Seite 137-150 volume:150 year:2010 number:1 day:27 month:05 pages:137-150 |
| sourceStr |
Enthalten in Geometriae dedicata 150(2010), 1 vom: 27. Mai, Seite 137-150 volume:150 year:2010 number:1 day:27 month:05 pages:137-150 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Geometriae dedicata |
| authorswithroles_txt_mv |
Jones, Rafe @@aut@@ Peters, Han @@aut@@ |
| publishDateDaySort_date |
2010-05-27T00:00:00Z |
| hierarchy_top_id |
129385301 |
| dewey-sort |
3510 |
| id |
OLC2039058923 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2039058923</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503063537.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2010 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10711-010-9499-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2039058923</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10711-010-9499-2-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jones, Rafe</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Blocks of monodromy groups in complex dynamics</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2010</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2010</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Iterated monodromy groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex dynamics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial iteration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Post-critically finite polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Conservative polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constant weighted sum of iterates</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Peters, Han</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Geometriae dedicata</subfield><subfield code="d">Springer Netherlands, 1972</subfield><subfield code="g">150(2010), 1 vom: 27. Mai, Seite 137-150</subfield><subfield code="w">(DE-627)129385301</subfield><subfield code="w">(DE-600)183909-3</subfield><subfield code="w">(DE-576)014772213</subfield><subfield code="x">0046-5755</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:150</subfield><subfield code="g">year:2010</subfield><subfield code="g">number:1</subfield><subfield code="g">day:27</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:137-150</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10711-010-9499-2</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_30</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4116</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">150</subfield><subfield code="j">2010</subfield><subfield code="e">1</subfield><subfield code="b">27</subfield><subfield code="c">05</subfield><subfield code="h">137-150</subfield></datafield></record></collection>
|
| author |
Jones, Rafe |
| spellingShingle |
Jones, Rafe ddc 510 ssgn 17,1 misc Iterated monodromy groups misc Complex dynamics misc Polynomial iteration misc Post-critically finite polynomials misc Conservative polynomials misc Constant weighted sum of iterates Blocks of monodromy groups in complex dynamics |
| authorStr |
Jones, Rafe |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129385301 |
| format |
Article |
| dewey-ones |
510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0046-5755 |
| topic_title |
510 VZ 17,1 ssgn Blocks of monodromy groups in complex dynamics Iterated monodromy groups Complex dynamics Polynomial iteration Post-critically finite polynomials Conservative polynomials Constant weighted sum of iterates |
| topic |
ddc 510 ssgn 17,1 misc Iterated monodromy groups misc Complex dynamics misc Polynomial iteration misc Post-critically finite polynomials misc Conservative polynomials misc Constant weighted sum of iterates |
| topic_unstemmed |
ddc 510 ssgn 17,1 misc Iterated monodromy groups misc Complex dynamics misc Polynomial iteration misc Post-critically finite polynomials misc Conservative polynomials misc Constant weighted sum of iterates |
| topic_browse |
ddc 510 ssgn 17,1 misc Iterated monodromy groups misc Complex dynamics misc Polynomial iteration misc Post-critically finite polynomials misc Conservative polynomials misc Constant weighted sum of iterates |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Geometriae dedicata |
| hierarchy_parent_id |
129385301 |
| dewey-tens |
510 - Mathematics |
| hierarchy_top_title |
Geometriae dedicata |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129385301 (DE-600)183909-3 (DE-576)014772213 |
| title |
Blocks of monodromy groups in complex dynamics |
| ctrlnum |
(DE-627)OLC2039058923 (DE-He213)s10711-010-9499-2-p |
| title_full |
Blocks of monodromy groups in complex dynamics |
| author_sort |
Jones, Rafe |
| journal |
Geometriae dedicata |
| journalStr |
Geometriae dedicata |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2010 |
| contenttype_str_mv |
txt |
| container_start_page |
137 |
| author_browse |
Jones, Rafe Peters, Han |
| container_volume |
150 |
| class |
510 VZ 17,1 ssgn |
| format_se |
Aufsätze |
| author-letter |
Jones, Rafe |
| doi_str_mv |
10.1007/s10711-010-9499-2 |
| dewey-full |
510 |
| title_sort |
blocks of monodromy groups in complex dynamics |
| title_auth |
Blocks of monodromy groups in complex dynamics |
| abstract |
Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. © The Author(s) 2010 |
| abstractGer |
Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. © The Author(s) 2010 |
| abstract_unstemmed |
Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics. © The Author(s) 2010 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4126 |
| container_issue |
1 |
| title_short |
Blocks of monodromy groups in complex dynamics |
| url |
https://doi.org/10.1007/s10711-010-9499-2 |
| remote_bool |
false |
| author2 |
Peters, Han |
| author2Str |
Peters, Han |
| ppnlink |
129385301 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s10711-010-9499-2 |
| up_date |
2024-07-03T21:24:11.443Z |
| _version_ |
1803594604428132352 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2039058923</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503063537.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2010 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10711-010-9499-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2039058923</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10711-010-9499-2-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jones, Rafe</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Blocks of monodromy groups in complex dynamics</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2010</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2010</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Iterated monodromy groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex dynamics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial iteration</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Post-critically finite polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Conservative polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constant weighted sum of iterates</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Peters, Han</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Geometriae dedicata</subfield><subfield code="d">Springer Netherlands, 1972</subfield><subfield code="g">150(2010), 1 vom: 27. Mai, Seite 137-150</subfield><subfield code="w">(DE-627)129385301</subfield><subfield code="w">(DE-600)183909-3</subfield><subfield code="w">(DE-576)014772213</subfield><subfield code="x">0046-5755</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:150</subfield><subfield code="g">year:2010</subfield><subfield code="g">number:1</subfield><subfield code="g">day:27</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:137-150</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10711-010-9499-2</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_30</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4116</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">150</subfield><subfield code="j">2010</subfield><subfield code="e">1</subfield><subfield code="b">27</subfield><subfield code="c">05</subfield><subfield code="h">137-150</subfield></datafield></record></collection>
|
| score |
7.4008274 |