Equicontinuity, transitivity and sensitivity

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• Joel Mitchell (University of Birmingham)
• Thursday 06 February 2020, 14:00-15:00
• Lecture Theater C, Watson Building.

If you have a question about this talk, please contact Simon Baker.

Robert Devaney defined chaos as a sensitive, transitive map where the set of periodic points is dense in the phase space. With an elegant proof, Banks et al showed that the the latter two properties entail the first. Since then, various analogues and generalisations of this result have been offered. Central to these theorems lie the notions of transitivity, equicontinuity, minimality and sensitivity.

In this talk I take a topological approach to dynamics and discuss sensitivity, topological equicontinuity and even continuity. I will 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. Time permitting, I will define what it means for a system to be eventually sensitive and give a dichotomy for transitive dynamical systems in relation to eventual sensitivity.

This talk is based upon joint work with Chris Good and Robert Leek. (See `Equicontinuity, transitivity and sensitivity: The Auslander-Yorke dichotomy revisited’ (2020) DCDS -A 40(4).)

This talk is part of the Topology and Dynamics Seminar series.

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• Lecture Theater C, Watson Building
• School of Mathematics Events
• Topology and Dynamics Seminar

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