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, R. (2012). A Characterization of topologically completely positive entropy for shifts of finite type. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/25