Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting - Avignon Université Access content directly
Journal Articles Ergodic Theory and Dynamical Systems Year : 2012

Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting

Abstract

We consider locally minimizing measures for the conservative twist maps of the $d$-dimensional annulus or for the Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic such measures (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and the unstable Oseledet's bundles gives an upper bound of the sum of the positive Lyapunov exponents and a lower bound of the smallest positive Lyapunov exponent. Some more precise results are proved too.
Fichier principal
Vignette du fichier
Lyapunovexponents2012.pdf (203.59 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-00572334 , version 1 (01-03-2011)
hal-00572334 , version 2 (23-01-2012)

Identifiers

Cite

Marie-Claude Arnaud. Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting. Ergodic Theory and Dynamical Systems, 2012, pp.1-20. ⟨10.1017/S0143385712000065⟩. ⟨hal-00572334v2⟩
261 View
207 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More