Chaos and mixing homeomorphisms on fans
Iztok Banic, Goran Erceg, Judy Kennedy, Chris Mouron, Van Nall
TL;DR
This paper constructs mixing homeomorphisms on specific fans, including the Lelek and Cantor fans, and introduces a large family of non-homeomorphic fans with such dynamics.
Contribution
It provides the first constructions of mixing homeomorphisms on these fans and introduces a vast family of non-homeomorphic fans with mixing dynamics.
Findings
Constructed mixing homeomorphisms on the Lelek and Cantor fans.
Established a family of uncountably many non-homeomorphic fans with mixing homeomorphisms.
Demonstrated the diversity of fan structures admitting mixing dynamics.
Abstract
We construct a mixing homeomorphism on the Lelek fan. We also construct a mixing homeomorphism on the Cantor fan. Then, we construct a family of uncountably many pairwise non-homeomorphic (non-)smooth fans that admit a mixing homeomorphism.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Nonlinear Dynamics and Pattern Formation · Quantum chaos and dynamical systems