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Lyapunov exponents in Hilbert geometry
Published online by Cambridge University Press: 03 December 2012
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.
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- ©2012 Cambridge University Press
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