Download or read book The Artin-Mazur Zeta Function of Interval Maps written by Jorge Olivares-Vinales and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this thesis 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, we prove that the zeta function is either rational or transcendental as a formal power series, and rationality or transcendence is characterized by the asymptotic behavior of the turning point. We use the theory of finite states automata for the proof. The rationality of the zeta function in this context was stated by Milnor and Thurston [Milnor and Thurston, 1988] without proof. Next, we show that for multimodal maps, the previous characterization does not hold."--Page ii.