In the case of negatively curved manifolds, unique equilibrium states
for the geodesic flow have the Bernoulli property, meaning that in one
sense, they are the "most random" they can be. However, for
equilibrium states in more general settings, proofs of uniqueness and
higher mixing properties often do not go hand in hand. I will discuss
methods for showing the K-property and the Bernoulli property for
unique equilibrium states in the setting of the geodesic flow on
translation surfaces, which is joint work with Dave Constantine, Alena
Erchenko, Noelle Sawyer, and Grace Work. The methods used are general
and can be applied elsewhere as well.
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