Exponential mixing for generic volume-preserving Anosov flows in   dimension three
  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. 
Masato Tsujii
math.DS