Hyperbolic Invariant Sets With Positive Measures
Dynamical Systems
2007-05-23 v2
Abstract
If a , , 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 , , Anosov diffeomorphism without the usual Hopf argument.
Cite
@article{arxiv.math/0503437,
title = {Hyperbolic Invariant Sets With Positive Measures},
author = {Zhihong Xia},
journal= {arXiv preprint arXiv:math/0503437},
year = {2007}
}