Average chain transitivity and the almost average shadowing property

TL;DR

This paper introduces new concepts related to average chain transitivity and shadowing in dynamical systems, exploring their properties and interrelations to deepen understanding of system behaviors.

Contribution

It defines and investigates average chain transitivity, mixing, and the almost average shadowing property, establishing their relationships and significance in dynamical systems theory.

Findings

Defined new notions of average chain transitivity and mixing.

Established relationships among the introduced properties.

Discussed implications for dynamical systems analysis.

Abstract

In this paper, we introduce and study notions of average chain transitivity, average chain mixing, total average chain transitivity and almost average shadowing property. We also discuss their interrelations.