# A Characterization of Topologically Completely Positive Entropy for Shifts of Finite Type

#### Abstract

A topological dynamical system was defined by Blanchard ([1]) to have topologically completely positive entropy (or t.c.p.e.) if its only zero entropy factor is the dynamical system consisting of a single fixed point. For Z d shifts of finite type, we give a simple condition equivalent to having topologically completely positive entropy. As an application, we use our characterization to derive a similar equivalent condition to t.c.p.e. for the subclass of Z group shifts, proved by Boyle and Schraudner in [3]. We also give an example of a Z shift of finite type which has topologically completely positive entropy but is not even topologically transitive.

### Cite this paper

@inproceedings{Pavlov2012ACO, title={A Characterization of Topologically Completely Positive Entropy for Shifts of Finite Type}, author={Ronnie Pavlov}, year={2012} }