English

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.

Keywords

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

R2 v1 2026-06-28T16:30:26.891Z