Dynamical systems with hyperbolic ("chaotic") behavior can be studied
from the statistical point of view by considering an invariant
probability measure. The space of such measures is very large and so
one arrives at the problem of selecting a measure that is most
dynamically relevant. For example, one can prove that there is a
unique measure of maximal entropy for transitive subshifts of finite
type, which code uniformly hyperbolic systems. I will describe two
approaches to this result: one via transfer operators and the other
via the specification property. If time permits I will explain how
these approaches generalize to other equilibrium states and to more
general classes of shift spaces.
Webmaster University of Houston
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Last modified: April 08 2016 - 20:30:35