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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Periodic points and smooth rays
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by Carsten Lunde Petersen and Saeed Zakeri
Conform. Geom. Dyn. 25 (2021), 170-178
Published electronically: October 27, 2021


Let $P: \mathbb {C} \to \mathbb {C}$ be a polynomial map with disconnected filled Julia set $K_P$ and let $z_0$ be a repelling or parabolic periodic point of $P$. We show that if the connected component of $K_P$ containing $z_0$ is non-degenerate, then $z_0$ 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 $z_0$ may be broken.
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Bibliographic Information
  • Carsten Lunde Petersen
  • Affiliation: Department of Mathematics, Roskilde University, DK-4000 Roskilde, Denmark
  • MR Author ID: 207550
  • ORCID: 0000-0002-4890-3183
  • Email:
  • Saeed Zakeri
  • Affiliation: Department of Mathematics, Queens College of CUNY, 65-30 Kissena Blvd., Queens, New York 11367; and The Graduate Center of CUNY, 365 Fifth Ave., New York, NY 10016
  • MR Author ID: 626230
  • Email:
  • Received by editor(s): February 26, 2021
  • Received by editor(s) in revised form: July 25, 2021
  • Published electronically: October 27, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 25 (2021), 170-178
  • MSC (2020): Primary 37F10, 37F25, 37F20
  • DOI:
  • MathSciNet review: 4332105