Zhihong Xia
Published 2005-03-21, updated 2005-08-26Version 2
If a $C^{1 + a}$, $a >0$, volume-preserving diffeomorphism on a compact manifold has a hyperbolic invariant set with positive volume, then the map is Anosov. We also give a direct proof of ergodicity of volume-preserving $CC^{1+a}$, $a>0$, Anosov diffeomorphism without the usual Hopf argument.
A direct proof of the existence of MME for finite horizon Sinai billiards
The Lyapunov exponents of generic volume preserving and symplectic systems
Exponential mixing implies Bernoulli
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