Hyperbolic Invariant Sets with Positive Measures
نویسنده
چکیده
In this note we prove some results concerning volume-preserving Anosov diffeomorphisms on compact manifolds. The main theorem is that if a C, α > 0, volume-preserving diffeomorphism on a compact manifold has a hyperbolic invariant set with positive volume, then the map is Anosov. This is not necessarily true for C maps. The proof uses a special type of measure density points different from the standard Lebesgue density points.
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