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arXiv · 2008.00328

Ergodicity and equidistribution in strictly convex Hilbert geometry

Feng Zhu
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Abstract

In this paper 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 geometrically-finite strictly convex projective structures equipped with their Hilbert metric. More specifically, such structures admit a finite Sullivan measure; with respect to this measure, the Hilbert geodesic flow is strongly mixing, and orbits and primitive closed geodesics equidistribute, allowing us to asymptotically enumerate these objects.

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Feng Zhu. 2020-08-01. Ergodicity and equidistribution in strictly convex Hilbert geometry. https://arxiv.org/abs/2008.00328

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