Hyperbolic invariant sets with positive measures
Hyperbolic invariant sets with positive measures
In this short paper we prove some results concerning volume-preservingAnosov diffeomorphisms on compact manifolds. The first theorem is thatif a $C^{1 + \alpha}$, $\alpha >0$, volume-preserving diffeomorphismon a compact connected manifold has a hyperbolic invariant set withpositive volume, then the map is Anosov. The same result had beenobtained by Bochi …