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.

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 \mathbfΔ_j and scalar multiplication by Δ_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

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