Exponential mixing for generic volume-preserving 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 $C^r$ volume-preserving Anosov flows on $M$ such that all the flows in it are exponentially mixing.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2016
- DOI:
- 10.48550/arXiv.1601.00063
- arXiv:
- arXiv:1601.00063
- Bibcode:
- 2016arXiv160100063T
- Keywords:
-
- Mathematics - Dynamical Systems;
- 37A25;
- 37D30;
- 37D20
- E-Print:
- 52 pages, 1 figure. A few errors in the previous version are corrected. Especially we fix errors in Section 4-6 that are caused by confusion between the non-conformal 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