Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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
HTML articles powered by AMS MathViewer

by Carsten Lunde Petersen and Saeed Zakeri PDF
Conform. Geom. Dyn. 25 (2021), 170-178 Request permission

Abstract:

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.
References
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2020): 37F10, 37F25, 37F20
  • Retrieve articles in all journals with MSC (2020): 37F10, 37F25, 37F20
Additional Information
  • Carsten Lunde Petersen
  • Affiliation: Department of Mathematics, Roskilde University, DK-4000 Roskilde, Denmark
  • MR Author ID: 207550
  • ORCID: 0000-0002-4890-3183
  • Email: lunde@ruc.dk
  • 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: saeed.zakeri@qc.cuny.edu
  • 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: https://doi.org/10.1090/ecgd/364
  • MathSciNet review: 4332105