Dynamical Systems Seminar

Equilibrium states are the canonical class of measures to consider in order to understand the statistical properties of a dynamical system. Indeed simply knowing that for some they exist and are unique already tells us something useful about the system. The classical approach to this problem is to find a finite symbolic coding for the dynamical system in question. In many nonuniformly hyperbolic situations useful codings can be difficult to uncover. In the case of quadratic interval maps I will explain that there is a countable symbolic coding and how the theory of Sarig on countable state Markov shifts can be applied to our interval maps to produce unique equilibrium states.