Renormalizations and Wandering Jordan Curves of Rational Maps
Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Cui, Guizhen [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 344(2016), 1 vom: 16. Apr., Seite 67-115 |
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| Übergeordnetes Werk: |
volume:344 ; year:2016 ; number:1 ; day:16 ; month:04 ; pages:67-115 |
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| DOI / URN: |
10.1007/s00220-016-2623-x |
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OLC2038912823 |
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| 520 | |a Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. | ||
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| 650 | 4 | |a Critical Cycle | |
| 700 | 1 | |a Peng, Wenjuan |4 aut | |
| 700 | 1 | |a Tan, Lei |4 aut | |
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10.1007/s00220-016-2623-x doi (DE-627)OLC2038912823 (DE-He213)s00220-016-2623-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Cui, Guizhen verfasserin aut Renormalizations and Wandering Jordan Curves of Rational Maps 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. Jordan Curve Jordan Domain Sierpinski Carpet Hyperbolic Component Critical Cycle Peng, Wenjuan aut Tan, Lei aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 344(2016), 1 vom: 16. Apr., Seite 67-115 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:344 year:2016 number:1 day:16 month:04 pages:67-115 https://doi.org/10.1007/s00220-016-2623-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 344 2016 1 16 04 67-115 |
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10.1007/s00220-016-2623-x doi (DE-627)OLC2038912823 (DE-He213)s00220-016-2623-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Cui, Guizhen verfasserin aut Renormalizations and Wandering Jordan Curves of Rational Maps 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. Jordan Curve Jordan Domain Sierpinski Carpet Hyperbolic Component Critical Cycle Peng, Wenjuan aut Tan, Lei aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 344(2016), 1 vom: 16. Apr., Seite 67-115 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:344 year:2016 number:1 day:16 month:04 pages:67-115 https://doi.org/10.1007/s00220-016-2623-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 344 2016 1 16 04 67-115 |
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10.1007/s00220-016-2623-x doi (DE-627)OLC2038912823 (DE-He213)s00220-016-2623-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Cui, Guizhen verfasserin aut Renormalizations and Wandering Jordan Curves of Rational Maps 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2016 Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. Jordan Curve Jordan Domain Sierpinski Carpet Hyperbolic Component Critical Cycle Peng, Wenjuan aut Tan, Lei aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 344(2016), 1 vom: 16. Apr., Seite 67-115 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:344 year:2016 number:1 day:16 month:04 pages:67-115 https://doi.org/10.1007/s00220-016-2623-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 344 2016 1 16 04 67-115 |
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Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. © Springer-Verlag Berlin Heidelberg 2016 |
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Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. © Springer-Verlag Berlin Heidelberg 2016 |
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Abstract We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations. © Springer-Verlag Berlin Heidelberg 2016 |
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