Syndetic proximality and scrambled sets

TL;DR

This paper systematically investigates syndetically proximal relations and scrambled sets in various dynamical systems, including subshifts, interval maps, and Anosov maps, providing new constructions and examples.

Contribution

It offers a comprehensive analysis of syndetically proximal relations and introduces new examples and constructions in different classes of dynamical systems.

Findings

Analysis of syndetically proximal relations in various systems

Existence or non-existence results for syndetically scrambled sets

New constructions and examples illustrating these phenomena

Abstract

This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of transitive subshifts, interval maps, and topologically Anosov maps. We also present many constructions and examples.