Entropy rigidity and flexibility for suspension flows over Anosov diffeomorphisms
Abstract
For any $C^\infty$, areapreserving Anosov diffeomorphism $f$ of a surface, we show that a suspension flow over $f$ is $C^\infty$conjugate to a constanttime suspension flow of a hyperbolic automorphism of the two torus if and only if the volume measure is the measure with maximal entropy. We also show that the the metric entropy with respect to the volume measure and the topological entropy of suspension flow over Anosov diffeomorphisms on torus achieve all possible values. Our results fit into two programs related to entropy rigidity and flexibility of Anosov systems.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1802.00145
 Bibcode:
 2018arXiv180200145B
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
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