Chaotic behavior of countable products of homeomorphism groups

TL;DR

This paper explores chaotic dynamics in countable products of homeomorphism groups, establishing new examples and relationships between chaos, transitivity, and orbit density in complex topological spaces.

Contribution

It introduces novel examples of chaotic homeomorphism groups on countable products of diverse metrizable spaces, including infinite-dimensional manifolds.

Findings

Established links between chaos and topological properties

Constructed new examples of chaotic groups on complex spaces

Analyzed properties of countable product groups

Abstract

Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We construct numerous new examples of chaotic groups of homeomorphisms of countable products of various metrizable topological spaces, including infinite-dimensional topological manifolds, whose factors can be as noncompact surfaces, so triangulable closed manifolds of an arbitrary dimension.