Entropies of compact strictly convex projective manifolds

Details Entropies of compact strictly convex projective manifolds Entropies of compact strictly convex projective manifolds

2009-04-16

arxiv.org/abs/0904.2489v1

Mathematics

Dynamical Systems

27 pages

Scientific paper

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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