Almost automorphy of invertible semiflows with compact Hausdorff phase spaces

Xiongping Dai

Published 2018-06-15Version 1

Let $T\times X\rightarrow X, (t,x)\mapsto tx$ be a minimal semiflow on a compact Hausdorff space $X$ with phase semigroup $T$ such that each $t\in T$ is an invertible map of $X$. An $x\in X$ is called an \textit{a.a. point} of $(T,X)$ if $(t_nx, t_n^{-1}y)\to(y, x^\prime)$ implies $x=x^\prime$ for every net $\{t_n\}$ in $T$. In this paper, we study the a.a. dynamics of invertible semiflows; and moreover, we first present a complete proof of Veech's structure theorem of an a.a. flow.