On dynamics of vertices of locally connected polynomial Julia sets

A. Blokh; G. Levin

doi:10.1090/S0002-9939-02-06698-4

On dynamics of vertices of locally connected polynomial Julia sets

A. Blokh^*
, G. Levin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let P be a polynomial whose Julia set J is locally connected. Then a non-preperiodic non-precritical vertex of J must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of P. In particular, if all critical points of P are non-recurrent then all vertices of J are preperiodic or precritical.

Original language	English
Pages (from-to)	3219-3230
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	130
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-02-06698-4
State	Published - 1 Nov 2002
Externally published	Yes

Keywords

Julia set
Laminations
Recurrent critical points
Vertices

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10.1090/S0002-9939-02-06698-4

Cite this

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abstract = "Let P be a polynomial whose Julia set J is locally connected. Then a non-preperiodic non-precritical vertex of J must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of P. In particular, if all critical points of P are non-recurrent then all vertices of J are preperiodic or precritical.",

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AU - Blokh, A.

AU - Levin, G.

PY - 2002/11/1

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N2 - Let P be a polynomial whose Julia set J is locally connected. Then a non-preperiodic non-precritical vertex of J must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of P. In particular, if all critical points of P are non-recurrent then all vertices of J are preperiodic or precritical.

AB - Let P be a polynomial whose Julia set J is locally connected. Then a non-preperiodic non-precritical vertex of J must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of P. In particular, if all critical points of P are non-recurrent then all vertices of J are preperiodic or precritical.

KW - Julia set

KW - Laminations

KW - Recurrent critical points

KW - Vertices

UR - https://www.scopus.com/pages/publications/0036842418

U2 - 10.1090/S0002-9939-02-06698-4

DO - 10.1090/S0002-9939-02-06698-4

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AN - SCOPUS:0036842418

SN - 0002-9939

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EP - 3230

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

On dynamics of vertices of locally connected polynomial Julia sets

Abstract

Keywords

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