13:30 - 14:30, November 6, 2025 (Thursday) Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
On the Artin-Mazur Zeta Functions for Dynamical Systems over Non-Archimedean Fields Liang-Chung Hsia (National Taiwan Normal University)
Abstract
Let be a complete non-archimedean field of characteristic with respect to a non-trivial valuation. In this talk, we will discuss the Artin-Mazur zeta function associated with dynamical system arising from iterations of a rational function defined over . We establish the rationality of the Artin-Mazur zeta function for the dynamics on the Julia set of subhyperbolic rational maps defined over with a compact Julia set. As a corollary, we conclude that the topological entropy on the Julia set of such a map is given by the logarithm of a weak Perron number. This is a joint work with Hongming Nie and Chenxi Wu.
