Almost automorphy of surjective semiflows on compact Hausdorff spaces

2018/06/15 by Dai, Xiongping
#20M20 #37B05 #37B20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05811

Abstract

Let (T,X) with phase mapping (t,x)↦ tx be a semiflow on a compact \textrmT₂-space X with phase semigroup T such that tX=X for each t of T. An x∈ X is called an a.a. point if t_nx→ y, x_n^′→ x^′ and t_nx_n^′=y implies x=x^′ for every net \t_n\ in T. In this paper, we study the a.a. dynamics of (T,X); and moreover, we present a complete proof of Veech's structure theorem for a.a. flows.

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