Shadowing, transitivity and a variation of omega-chaos

TL;DR

This paper investigates a specific shadowing property in chain transitive systems, establishing conditions for a statistical form of omega-chaos and demonstrating its genericity, along with analyzing irregular points' distribution.

Contribution

It introduces and studies a special shadowing property (DSP), providing new conditions for statistical omega-chaos and its topological genericity in compact spaces.

Findings

DSP has fundamental properties and implications.

Sufficient conditions for statistical omega-chaos are established.

Statistical omega-chaos is topologically generic under DSP.

Abstract

We study a special type of shadowing (DSP) of chain transitive continuous self-maps of compact Hausdorff spaces. We prove some basic properties of DSP. As application of DSP, we obtain sufficient conditions for a statistical variant of $\omega$-chaos and prove the topological genericity of it. We also consider topological distribution of irregular points under the assumption of DSP.