The Artin-Mazur zeta function for interval maps
Dynamical Systems
2024-05-21 v2
Abstract
In this work we study the Artin-Mazur zeta function for piecewise monotone functions acting on a compact interval of real numbers. In the case of unimodal maps, Milnor and Thurston gave a characterization for the rationality of the Artin-Mazur zeta function in terms of the orbit of the unique turning point. We show that for multimodal maps, the previous characterization does not hold.
Cite
@article{arxiv.2405.10560,
title = {The Artin-Mazur zeta function for interval maps},
author = {Jorge Olivares-Vinales},
journal= {arXiv preprint arXiv:2405.10560},
year = {2024}
}
Comments
33 pages, 7 figures