Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



Return times of polynomials as meta-Fibonacci numbers

Author: Nathaniel D. Emerson
Journal: Conform. Geom. Dyn. 12 (2008), 153-173
MSC (2000): Primary 37F10, 37F50; Secondary 11B39
Published electronically: October 14, 2008
MathSciNet review: 2448263
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 37F10, 37F50, 11B39

Retrieve articles in all journals with MSC (2000): 37F10, 37F50, 11B39

Additional Information

Nathaniel D. Emerson
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089

Keywords: Julia set, meta-Fibonacci, polynomial, principal nest, puzzle, return time, tree with dynamics.
Received by editor(s): December 10, 2007
Published electronically: October 14, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.