Hyperbolic Invariant Sets With Positive Measures

Details Hyperbolic Invariant Sets With Positive Measures Hyperbolic Invariant Sets With Positive Measures

2005-03-21

arxiv.org/abs/math/0503437v2

Mathematics

Dynamical Systems

Scientific paper

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.

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