Topological entropy on set-valued functions

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.