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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- Nathaniel D. Emerson
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
- Email: firstname.lastname@example.org
- 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