%0 Journal Article
%T Hyperbolic Invariant Sets With Positive Measures
%A Zhihong Xia
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0503437v2