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• W3046874303 abstract "We show that dynamical and counting results characteristic of negatively-curved Riemannian geometry, or more generally CAT($-1$) or rank-one CAT($0$) spaces, also hold for rank-one properly convex projective structures, equipped with their Hilbert metrics, admitting finite Sullivan measures built from appropriate conformal densities. In particular, this includes geometrically finite convex projective structures. More specifically, with respect to the Sullivan measure, the Hilbert geodesic flow is strongly mixing, and orbits and primitive closed geodesics equidistribute, allowing us to asymptotically enumerate these objects." @default.
• W3046874303 created "2020-08-07" @default.
• W3046874303 creator A5002672002 @default.
• W3046874303 creator A5041930545 @default.
• W3046874303 date "2021-06-15" @default.
• W3046874303 modified "2023-09-27" @default.
• W3046874303 title "Ergodicity and equidistribution in Hilbert geometry" @default.
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• W3046874303 doi "https://doi.org/10.48550/arxiv.2106.08079" @default.
• W3046874303 hasPublicationYear "2021" @default.
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