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Daniel Thompson (Ohio State University)

Three lectues on: Weak specification properties in symbolic and smooth dynamics

Lecture 1: 11am Tuesday 28 July 2015, Room B3.02

Abstract: An introductory discussion of the specification property in symbolic and smooth dynamical systems. The aim is to give an overview of the plethora of weak specification properties currently available in the literature, and what they are good for.

Lecture 2: 11am Wednesday 29 July 2015, Room B3.02

Abstract: I will describe how the ‘specification approach’ can be used to establish the uniqueness of the measure of maximal entropy for beta-shifts, and factors of beta-shifts. This result was the initial motivation for a series of papers by myself and Vaughn Climenhaga (Houston).

Lecture 3: 11am Thursday 30 July 2015, Room B3.02

Abstract: We have recently adapted the techniques described in Lecture 2 to a large class of smooth dynamical systems beyond uniform hyperbolicity. Settings where our techniques apply include geodesic flow on non-positive curvature manifolds, and certain model examples of diffeomorphisms with partial hyperbolicity, or dominated splittings (introduced by Mañé and Bonatti-Viana respectively). I’ll describe some of these results, and the techniques that drive them. This is joint work with Keith Burns, Vaughn Climenhaga and Todd Fisher.