EVENT DETAILS AND ABSTRACT

Title: Entropies realizable in block gluing Z^d shifts of finite type
Speaker: Michael Schraudner
Speaker Info: University of Chile
Brief Description:
Special Note:
Abstract:

Hochman and Meyerovitch gave a complete characterization of the topological entropies appearing in Z^d shifts of finite type (SFTs) for any d>1. Nevertheless their method of construction is quiet rigid and yields only relatively degenerate Z^d SFTs lacking any (uniform) mixing property and being a specific extension of a non-trivial zero-entropy subshift factor. In this talk - after giving some basic definitions and explaining some background on uniform mixing properties like block gluing - we will give a necessary condition for a real number to be realizable as the topological entropy of a block gluing Z^d SFT. Subsequently we will present a new technique - combining an elaboration of the Hochman-Meyerovitch construction with two new ideas - to actually realize a large class of well-behaved real numbers as entropies of block gluing Z^d SFTs for any d>2. As a final corollary we get a result about the non-existence of certain entropy-preserving Z^d full-shift factors in the presence of block gluing. The presented results are recent joint work with Ronnie Pavlov.