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 | Leave a comment

Alpha-beta shifts

Given , the interval map given by is naturally semi-conjugate to the -shift . The shift space admits a natural description in terms of the lexicographic order, and another in terms of a countable-state directed graph. These have been used … Continue reading

Posted in ergodic theory, examples, Uncategorized | 2 Comments