Lyapunov exponents in Hilbert geometry
Dynamical Systems
2019-02-20 v1 Differential Geometry
Metric Geometry
Abstract
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.
Cite
@article{arxiv.1105.6275,
title = {Lyapunov exponents in Hilbert geometry},
author = {Mickaël Crampon},
journal= {arXiv preprint arXiv:1105.6275},
year = {2019}
}
Comments
34 pages, comments are welcome