Entropies of Compact Strictly Convex Projective Manifolds
نویسنده
چکیده
Let M be a compact manifold of dimension n with a strictly convex projective structure. We consider the geodesic flow of the Hilbert metric on it which is known to be Anosov. We prove that its topological entropy is less than n − 1, with equality if and only if the structure is Riemannian, that is hyperbolic. As a corollary, we get that the volume entropy of a divisible strictly convex set is less than n − 1, with equality if and only if it is an ellipsoid.
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تاریخ انتشار 2009