arXiv subjects

Tim Tennant

Publications and source records attributed to Tim Tennant.

2 recordsLinked to original sources

arXiv2015

Topological entropy on set-valued functions

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.

math.DS↗

arXiv2015

The specification property on a set-valued map and its inverse limit

In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and prove some elementary results of these properties. We end with a few results regarding invariant measures for set-valued functions and their associated inverse limits.

math.DS↗