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arXiv · 1903.09060

Equicontinuity, Transitivity and Sensitivity: the Auslander-Yorke Dichotomy Revisited

Chris Good·Robert Leek·Joel Mitchell
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Abstract

We discuss topological equicontinuity and even continuity in dynamical systems. In doing so we provide a classification of topologically transitive dynamical systems in terms of equicontinuity pairs, give a generalisation of the Auslander-Yorke Dichotomy for minimal systems and show there exists a transitive system with an even continuity pair but no equicontinuity point. We define what it means for a system to be eventually sensitive; we give a dichotomy for transitive dynamical systems in relation to eventual sensitivity. Along the way we define a property called splitting and discuss its relation to some existing notions of chaos.

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Chris Good, Robert Leek, Joel Mitchell. 2019-03-21. Equicontinuity, Transitivity and Sensitivity: the Auslander-Yorke Dichotomy Revisited. https://doi.org/10.3934/dcds.2020121

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