Seminar 11.10.16 Pavlov

Title: Weakened specification properties and intrinsic ergodicity for subshifts

Speaker: Ronnie Pavlov (University of Denver)

Abstract: The specification property has been fundamental in the study of topological dynamical systems since its introduction by Bowen, and among other properties, implies intrinsic ergodicity, i.e. uniqueness of the measure of maximal entropy. For subshifts, specification amounts to the ability to concatenate arbitrary pairs of n-letter words given a uniform gap (i.e. independent of n).

In this setting, several natural weakenings of specification can be defined. For instance, one can allow non-uniform gaps, or allow a small number of “edits” to the words rather than including a gap. In both cases, one can parametrize by an auxiliary function f(n) controlling gap size/number of edits.

I will summarize some recent results in this area, beginning with examples showing that several weakened specification properties do not imply intrinsic ergodicity even for slowly growing f(n), and finishing with recent joint work with Vaughn Climenhaga, in which we defined a new weakened specification property which does imply intrinsic ergodicity for small enough f(n).