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Monthly Archives: June 2017
Gibbs measures have local product structure
Let be a compact smooth manifold and a transitive Anosov diffeomorphism. If is an invariant Borel probability measure on that is absolutely continuous with respect to volume, then the Hopf argument can be used to show that is ergodic. In … Continue reading
Posted in ergodic theory, smooth dynamics
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Alphabeta shifts
Given , the interval map given by is naturally semiconjugate to the shift . The shift space admits a natural description in terms of the lexicographic order, and another in terms of a countablestate directed graph. These have been used … Continue reading
Posted in ergodic theory, examples, Uncategorized
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