Arithmetic and growth of periodic orbits
Dynamical Systems
2007-05-23 v2 Number Theory
Abstract
We give necessary and sufficient conditions for a sequence to be exactly realizable as the sequence of numbers of periodic points in a dynamical system. Using these conditions, we show that no non-constant polynomial is realizable, and give some conditions on realizable binary recurrence sequences. Realization in rate is always possible for sufficiently rapidly-growing sequences, and is never possible for slowly-growing sequences. Finally, we discuss the relationship between the growth rate of periodic points and the growth rate of points with specified least period.
Cite
@article{arxiv.math/9907003,
title = {Arithmetic and growth of periodic orbits},
author = {Yash Puri and Thomas Ward},
journal= {arXiv preprint arXiv:math/9907003},
year = {2007}
}
Comments
Revised version with new content; to appear in J.Integer Sequences