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Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting

Published online by Cambridge University Press:  17 April 2012

M.-C. ARNAUD
M.-C. ARNAUD*
Affiliation:
Laboratoire d’Analyse non linéaire et Géométrie (EA 2151), Université d’Avignon et des Pays de Vaucluse, F-84 018 Avignon, France (email: Marie-Claude.Arnaud@univ-avignon.fr)
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Abstract

We consider locally minimizing measures for conservative twist maps of the $d$-dimensional annulus and for Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic measures of such type (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and unstable Oseledets bundles gives an upper bound on the sum of the positive Lyapunov exponents and a lower bound on the smallest positive Lyapunov exponent. We also prove some more precise results.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 3 , June 2013 , pp. 693 - 712
Copyright
Copyright © 2012 Cambridge University Press

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