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arXiv · 2405.10560

The Artin-Mazur zeta function for interval maps

Jorge Olivares-Vinales
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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.

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Jorge Olivares-Vinales. 2024-05-17. The Artin-Mazur zeta function for interval maps. https://arxiv.org/abs/2405.10560

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