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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.


Return times of polynomials as meta-Fibonacci numbers
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by Nathaniel D. Emerson
Conform. Geom. Dyn. 12 (2008), 153-173
Published electronically: October 14, 2008


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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Bibliographic Information
  • Nathaniel D. Emerson
  • Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
  • Email:
  • 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:
  • MathSciNet review: 2448263