Hausdorff dimension of quadratic rational Julia sets
Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two.
Autor*in: |
Zhou, Jia [verfasserIn] |
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Artikel |
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Sprache: |
Englisch |
Erschienen: |
2013 |
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Schlagwörter: |
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Anmerkung: |
© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 |
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Übergeordnetes Werk: |
Enthalten in: Acta mathematica sinica - Springer Berlin Heidelberg, 1985, 30(2013), 2 vom: 24. Mai, Seite 331-342 |
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Übergeordnetes Werk: |
volume:30 ; year:2013 ; number:2 ; day:24 ; month:05 ; pages:331-342 |
Links: |
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DOI / URN: |
10.1007/s10114-013-1640-3 |
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OLC2062517971 |
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10.1007/s10114-013-1640-3 doi (DE-627)OLC2062517971 (DE-He213)s10114-013-1640-3-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Zhou, Jia verfasserin aut Hausdorff dimension of quadratic rational Julia sets 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. Shallow Julia sets quadratic rational map Hausdorff dimension Liao, Liang Wen aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 30(2013), 2 vom: 24. Mai, Seite 331-342 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:30 year:2013 number:2 day:24 month:05 pages:331-342 https://doi.org/10.1007/s10114-013-1640-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 AR 30 2013 2 24 05 331-342 |
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10.1007/s10114-013-1640-3 doi (DE-627)OLC2062517971 (DE-He213)s10114-013-1640-3-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Zhou, Jia verfasserin aut Hausdorff dimension of quadratic rational Julia sets 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. Shallow Julia sets quadratic rational map Hausdorff dimension Liao, Liang Wen aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 30(2013), 2 vom: 24. Mai, Seite 331-342 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:30 year:2013 number:2 day:24 month:05 pages:331-342 https://doi.org/10.1007/s10114-013-1640-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 AR 30 2013 2 24 05 331-342 |
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10.1007/s10114-013-1640-3 doi (DE-627)OLC2062517971 (DE-He213)s10114-013-1640-3-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Zhou, Jia verfasserin aut Hausdorff dimension of quadratic rational Julia sets 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. Shallow Julia sets quadratic rational map Hausdorff dimension Liao, Liang Wen aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 30(2013), 2 vom: 24. Mai, Seite 331-342 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:30 year:2013 number:2 day:24 month:05 pages:331-342 https://doi.org/10.1007/s10114-013-1640-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 AR 30 2013 2 24 05 331-342 |
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Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 |
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Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 |
abstract_unstemmed |
Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two. © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2062517971</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502172617.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10114-013-1640-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2062517971</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10114-013-1640-3-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="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">Zhou, Jia</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Hausdorff dimension of quadratic rational Julia sets</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</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">© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. 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