[20191108 : Colloquium] Towards the ergodcity of p-adic dynamical systems

1. 일시 : 2019118() 오후 430~ 530

2. 장소 : 아산이학관 526

3. 연사 : 정상태(인하대학교 수학과, 교수)

4. 제목 : Towards the ergodcity of p-adic dynamical systems

5. 내용 : Dynamical systems on non-Archimedean local rings are mainly classified as a dichotomy between 1-Lipschitz functions and expansive functions. In this talk, we introduce basics of non-Archimedean dynamics and provide some criteria for measure-preservation/ergodicity/Bernoullicity criterion of the two types of functions on the ring Zp of p-adic integers. As a main result, we provide a complete ergodic decomposition of a class of certain 1-Lipschitz functions on Z using linearization arguments which play a great role in the study of ergodicity criteria of f, along with two well-known bases of van der Put and Mahler in the expansion of such a function f.