An uncountable family of smooth fans that admit transitive homeomorphisms
Iztok Banic, Goran Erceg, Judy Kennedy, Chris Mouron, Van, Nall
TL;DR
This paper constructs an uncountable family of smooth fans with transitive homeomorphisms and demonstrates transitivity in the star of Cantor fans, expanding understanding of dynamical properties in topological spaces.
Contribution
It introduces a large family of smooth fans with transitive homeomorphisms and shows transitivity in the star of Cantor fans, which was previously unestablished.
Findings
Uncountably many non-homeomorphic smooth fans admit transitive homeomorphisms.
The star of Cantor fans admits a transitive homeomorphism.
Provides new examples of topological spaces with transitive dynamics.
Abstract
We construct a family of uncountably many pairwise non-homeomorphic smooth fans that admit transitive homeomorphisms. In addition, we show that the star of Cantor fans admits a transitive homeomorphism.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic and geometric function theory · Advanced Differential Equations and Dynamical Systems