On transitivity dynamics of topological semiflows

TL;DR

This paper explores various aspects of transitivity dynamics in topological semiflows, analyzing how the phase semigroup influences the behavior of the system.

Contribution

It introduces and discusses new concepts and results related to transitivity in topological semiflows, expanding understanding of their dynamical properties.

Findings

Different types of transitivity are characterized and compared.

Conditions under which transitivity properties hold are identified.

Implications for the structure of semiflows are discussed.

Abstract

Let $T\times X\rightarrow X, (t,x)\mapsto tx$, be a topological semiflow on a topological space $X$ with phase semigroup $T$. We introduce and discuss in this paper various transitivity dynamics of $(T,X)$.