Lyapunov exponents in Hilbert geometry

Mickaël Crampon (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We study the behaviour of a Hilbert geometry when going to infinity along a geodesic line. We prove that all the information is contained in the shape of the boundary at the endpoint of this geodesic line and have to introduce a regularity property of convex functions to make this link precise. The point of view is a dynamical one and the main interest of this article is in Lyapunov exponents of the geodesic flow.

Mots clés: Hilbert geometry; Lyapunov exponents; Hyperbolic dynamics

Domaines: Systèmes dynamiques [math.DS]; Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Mickaël Crampon. Lyapunov exponents in Hilbert geometry. Ergodic Theory and Dynamical Systems, 2014, 34, pp.501-533. ⟨10.1017/etds.2012.145⟩. ⟨hal-00596998v2⟩