Periodic points and smooth rays

Carsten Lunde Petersen; Saeed Zakeri

doi:10.1090/ECGD/364

Periodic points and smooth rays

Carsten Lunde Petersen^*, Saeed Zakeri

^*Corresponding author for this work

Department of Science and Environment

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

Let P: (Formula presented) be a polynomial map with disconnected filled Julia set KP and let z0 be a repelling or parabolic periodic point of P.Weshow that if the connected component of KP containing z0 is non-degenerate, then z0 is the landing point of at least one smooth external ray. The statement is optimal in the sense that all but one cycle of rays landing at z0 may be broken.

Original language	English
Journal	Conformal Geometry and Dynamics
Volume	25
Issue number	8
Pages (from-to)	170-178
Number of pages	9
DOIs	https://doi.org/10.1090/ECGD/364
Publication status	Published - 2021

Bibliographical note

This article has beeen found as a 'Free version' at the Publisher on November 30, 2021. When access closes, please contact [email protected]

Link to document

10.1090/ECGD/364

Periodic points and smooth raysAccepted author manuscript, 851 KBLicence: CC BY-NC-ND

Cite this

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PY - 2021

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N2 - Let P: (Formula presented) be a polynomial map with disconnected filled Julia set KP and let z0 be a repelling or parabolic periodic point of P.Weshow that if the connected component of KP containing z0 is non-degenerate, then z0 is the landing point of at least one smooth external ray. The statement is optimal in the sense that all but one cycle of rays landing at z0 may be broken.

AB - Let P: (Formula presented) be a polynomial map with disconnected filled Julia set KP and let z0 be a repelling or parabolic periodic point of P.Weshow that if the connected component of KP containing z0 is non-degenerate, then z0 is the landing point of at least one smooth external ray. The statement is optimal in the sense that all but one cycle of rays landing at z0 may be broken.

UR - https://www.ams.org/journals/ecgd/2021-25-08/S1088-4173-2021-00364-7/S1088-4173-2021-00364-7.pdf

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JO - Conformal Geometry and Dynamics

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Periodic points and smooth rays

Abstract

Bibliographical note

Link to document

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Cite this