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
Autor*in: |
Jones, Rafe [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2010 |
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Schlagwörter: |
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Anmerkung: |
© The Author(s) 2010 |
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Übergeordnetes Werk: |
Enthalten in: Geometriae dedicata - Springer Netherlands, 1972, 150(2010), 1 vom: 27. Mai, Seite 137-150 |
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Übergeordnetes Werk: |
volume:150 ; year:2010 ; number:1 ; day:27 ; month:05 ; pages:137-150 |
Links: |
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DOI / URN: |
10.1007/s10711-010-9499-2 |
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OLC2039058923 |
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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. | ||
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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 |
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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 |
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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 |
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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 |
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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 |
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title_short |
Blocks of monodromy groups in complex dynamics |
url |
https://doi.org/10.1007/s10711-010-9499-2 |
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Peters, Han |
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up_date |
2024-07-03T21:24:11.443Z |
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