The Artin-Mazur zeta function for interval maps

2024/05/17 by Olivares-Vinales, Jorge
#37E05 #37E15 #37F44 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.10560

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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