Existence and uniqueness of equilibria for non-uniformly hyperbolic dynamical systems
January 29, 4pm
646 PGH
Abstract
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.
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Last modified: April 08 2016 - 20:30:35