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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.

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Return times of polynomials as meta-Fibonacci numbers
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by Nathaniel D. Emerson PDF
Conform. Geom. Dyn. 12 (2008), 153-173 Request permission

Abstract:

We consider generalized closest return times of a complex polynomial of degree at least two. Most previous studies on this subject have focused on the properties of polynomials with particular return times, especially the Fibonacci numbers. We study the general form of these closest return times. The main result of this paper is that these closest return times are meta-Fibonacci numbers. In particular, this result applies to the return times of a principal nest of a polynomial. Furthermore, we show that an analogous result holds in a tree with dynamics that is associated with a polynomial.
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Additional Information
  • Nathaniel D. Emerson
  • Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
  • Email: nemerson@usc.edu
  • Received by editor(s): December 10, 2007
  • Published electronically: October 14, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 12 (2008), 153-173
  • MSC (2000): Primary 37F10, 37F50; Secondary 11B39
  • DOI: https://doi.org/10.1090/S1088-4173-08-00183-5
  • MathSciNet review: 2448263