Chaotic behaviour of countable products of homeomorphism groups

ABSTRACT

Relationships between a chaotic behaviour 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 provide a large number of 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.

KEYWORDS:

• Chaotic group of homeomorphisms
• sensitive dependence on initial conditions
• topological transitivity
• product of groups
• Tychonoff product

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 37B05
• 54H15
• 54E52
• 37E40
• 57M60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by Russian Science Foundation, project No 22-21-00304.