Strongly distributional chaos in the sets of twelve different types of non-recurrent points

TL;DR

This paper demonstrates that various types of non-recurrent points in certain dynamical systems exhibit strong distributional chaos, indicating high complexity in their statistical structures.

Contribution

It introduces twelve different types of non-recurrent points and proves their associated statistical structures are strongly distributionally chaotic in mixing expanding maps and transitive Anosov diffeomorphisms.

Findings

All twelve types exhibit strong distributional chaos.

The results apply to mixing expanding maps and transitive Anosov diffeomorphisms.

The study reveals high dynamical complexity of non-recurrent points.

Abstract

In present paper we mainly focus on non-recurrent dynamical orbits with empty syndetic center and show that twelve different statistical structures over mixing expanding maps or transitive Anosov diffeomorphisms all have dynamical complexity in the sense of strongly distributional chaos.