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Lyapunov exponents in Hilbert geometry

Published online by Cambridge University Press:  03 December 2012

MICKAËL CRAMPON
MICKAËL CRAMPON*
Affiliation:
Universidad de Santiago de Chile, Av. El Belloto 3580, Estación Central, Santiago de Chile, Chile (email: mickael.crampon@usach.cl)
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Abstract

We study the Lyapunov exponents of the geodesic flow of a Hilbert geometry. We prove that all of the information is contained in the shape of the boundary at the endpoint of the chosen orbit. We have to introduce a regularity property of convex functions to make this link precise. As a consequence, Lyapunov manifolds tangent to the Lyapunov splitting appear very easily. All of this work can be seen as a consequence of convexity and the flatness of Hilbert geometries.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 2 , April 2014 , pp. 501 - 533
Copyright
©2012 Cambridge University Press 

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