Chaos and mixing homeomorphisms on fans

We construct a mixing homeomorphism on both the Lelek fan and the Cantor fan. We also construct a family of uncountably many pairwise non-homeomorphic smooth (and non-smooth) fans that admit mixing homeomorphisms.

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Bibliographic Details
Published in:Journal of difference equations and applications 2025-01, Vol.31 (1), p.1-31
Main Authors: Banič, Iztok, Erceg, Goran, Kennedy, Judy, Mouron, Chris, Nall, Van
Format: Article
Language:English
Subjects:
Closed relations
Mahavier products
mixing homeomorphisms
smooth fan
transitive dynamical systems
transitive homeomorphisms
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Description
Summary:We construct a mixing homeomorphism on both the Lelek fan and the Cantor fan. We also construct a family of uncountably many pairwise non-homeomorphic smooth (and non-smooth) fans that admit mixing homeomorphisms.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2024.2384947