Colloquium / Seminars
Topic:Topologically Mixing Properties of Multiplicative Integer System
Speaker:Prof. Chih-Hung Chang
(Dept. of Applied Mathematics, National University of Kaosiung)Date time:May 12, 2020 14:00-15:00
Venue:SA223
Abstract:
Abstract. Motivated from the study of multiple ergodic average, the investigation of multiplicative shift spaces has caused researcher's interests. In this talk, I will introduce the relations of topologically mixing properties of multiplicative shift spaces and traditional shift spaces, which are additively invariant. Suppose that $\mathsf{X}_{\Omega}^{(l)}$ is the multiplicative subshift comes from the shift space $\Omega$ with given $l > 1$. We show that $\mathsf{X}_{\Omega}^{(l)}$ is (topologically) transitive/mixing if and only if $\Omega$ is extensible/mixing. After introducing $l$-directional mixing property, we derive the equivalence between $l$-directional mixing property of $\mathsf{X}_{\Omega}^{(l)}$ and weakly mixing property of $\Omega$.
***本演講為遠距同步演講***Download:TALK_1090512.pdf
go back