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Return times of polynomials as meta-Fibonacci numbers
Author(s):
Nathaniel
D.
Emerson
Journal:
Conform. Geom. Dyn.
12
(2008),
153-173.
MSC (2000):
Primary 37F10, 37F50;
Secondary 11B39
Posted:
October 14, 2008
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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
DOI:
10.1090/S1088-4173-08-00183-5
PII:
S 1088-4173(08)00183-5
Keywords:
Julia set,
meta-Fibonacci,
polynomial,
principal nest,
puzzle,
return time,
tree with dynamics.
Received by editor(s):
December 10, 2007
Posted:
October 14, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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