Topological completely positive entropy; shift of finite type; multidimensional.
A topological dynamical system was defined by Blanchard () 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 d group shifts, proved by Boyle and Schraudner in . We also give an example of a Z 2 shift of finite type which has topologically completely positive entropy but is not even topologically transitive.
Pavlov, Ronnie, "A Characterization of Topologically Completely Positive Entropy for Shifts of Finite Type" (2012). Mathematics Preprint Series. 25.