Chaotic properties of set-valued dynamical systems.

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Access changed 7/12/18.

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Abstract

In this thesis, many classical results of topological dynamics are adapted to the set-valued case. In particular, focus is given to the notions of topological entropy and the specification property. These properties are defined in the context of set-valued functions, and examples are given both of classical theorems that extend naturally to this setting and of theorems which have no clear analogue. Particular attention is paid to a result which states that if a dynamical system has the specification property, there exists invariant non-atomic measures with full support.

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Topological chaos. Set-valued dynamical systems. Set-valued inverse limits. Specification property. Topological entropy.

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