Entropies of compact strictly convex projective manifolds

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dc.creatorCrampon, Mickaël
dc.date2009-04-16
dc.date.accessioned2026-07-07T13:05:01Z
dc.date.available2026-07-07T13:05:01Z
dc.descriptionLet 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.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/0904.2489
dc.identifierhttp://arxiv.org/abs/0904.2489
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227368
dc.subjectDynamical Systems
dc.subjectDifferential Geometry
dc.titleEntropies of compact strictly convex projective manifolds
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