Exponential mixing for generic volumepreserving Anosov flows in dimension three
Abstract
Let $M$ be a closed $3$dimensional Riemann manifold and let $3\le r\le \infty$. We prove that there exists an open dense subset in the space of $C^r$ volumepreserving Anosov flows on $M$ such that all the flows in it are exponentially mixing.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.00063
 Bibcode:
 2016arXiv160100063T
 Keywords:

 Mathematics  Dynamical Systems;
 37A25;
 37D30;
 37D20
 EPrint:
 52 pages, 1 figure. A few errors in the previous version are corrected. Especially we fix errors in Section 46 that are caused by confusion between the nonconformal linear map \mathbf{\Delta}_j and scalar multiplication by \Delta_j. Also we modified the Definition 6.14 to resolve a small error in Lemma 6.6. Besides we give more details of the argument and fix several minor errors and typos