一、課程背景與目的：

The aim of ergodic theory is to understand the stochastic behavior of deterministic dynamical systems by studying the ergodic invariant probability measures of the system. Given such a measure, the ergodic theorems provide quantitative information on the long term behavior of almost every orbit. Ergodic theory has been widely applied to many disciplines such as number theory, ecological systems, and complex analysis. In this course, we will introduce thermodynamic formalism on countable Markov shifts. Meanwhile, the theory of symbolic dynamics and cellular automata on amenable groups will also be discussed. Amenability, which originated from the study of the Banach-Tarski paradox, is a property of groups generalizing both commutativity and finiteness. Nowadays, it plays an important role in many areas of mathematics.

二、課程之大綱與講者：

Lecturer: Prof. Jung-Chao Ban (jcban@nccu.edu.tw)

Department of Mathematical Sciences, National Chengchi University

Date:Sep. 18-Oct. 16, 2020(no class on 10/2 & 10/9, 3 weeks in total)

Title: Countable state topological Markov shifts

Lecturer: Prof. Chih-Hung Chang(chchang@nuk.edu.tw)

Department of Applied Mathematics, National University of Kaohsiung

Date:Oct. 23, 2020-Jan. 15, 2021(no class on 11/20, 12 weeks in total)

Title: Cellular automata and amenable groups

三、課程詳細時間地點以及方式：

Every Friday 10:10-12:00 pm, 13:10-14:00 pm

Lecture Room R201, Astronomy-Mathematics Building, NTU(To be confirmed)