When is weakly almost periodic equivalent to uniformly almost periodic for semiflows?

TL;DR

This paper investigates conditions under which weakly almost periodic semiflows on compact spaces are equivalent to uniformly almost periodic or equicontinuous, clarifying their relationships in dynamical systems.

Contribution

It establishes specific conditions that determine when weakly almost periodic semiflows are equivalent to uniformly almost periodic or equicontinuous.

Findings

Identifies conditions for equivalence between weakly and uniformly almost periodic semiflows.

Provides criteria linking weakly almost periodicity to equicontinuity.

Enhances understanding of the structure of semiflows on compact spaces.

Abstract

Let $\pi\colon T\times X\rightarrow X$ be a semiflow on a compact Hausdorff space $X$ with phase semigroup $T$. This paper provides us with some conditions under which \textsl{weakly almost periodic} is equivalent to \textsl{uniformly almost periodic} or to \textsl{equicontinuous} for $(T,X,\pi)$.