Topological entropy on set-valued functions

James Kelly; Tim Tennant

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arXiv · 1509.08413

Topological entropy on set-valued functions

James Kelly·Tim Tennant

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Abstract

Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known results concerning topological entropy of continuous (single-valued) functions extend naturally to set-valued functions while others must be altered. We also present sufficient conditions for a set-valued function to have positive or infinite topological entropy.

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James Kelly, Tim Tennant. 2015-09-28. Topological entropy on set-valued functions. https://arxiv.org/abs/1509.08413

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