Lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions

Abstract : The globally positive diffeomorphisms of the 2n-dimensional annulus are important because they represent what happens close to a completely elliptic periodic point of a symplectic diffeomorphism where the torsion is positive definite. For these globally positive diffeomorphisms, an Aubry-Mather theory was developed by Garibaldi & Thieullen that provides the existence of some minimizing measures. Using the two Green bundles G- and G+ that can be defined along the support of these minimizing measures, we will prove that there is a deep link between: -the angle between G- and G+ along the support of the considered measure m; -the size of the smallest positive Lyapunov exponent of m; -the tangent cone to the support of m.
Type de document :
Article dans une revue
Communications in Mathematical Physics, Springer Verlag, 2016, 343 (3), pp.783-810
Liste complète des métadonnées

https://hal-univ-avignon.archives-ouvertes.fr/hal-01065120
Contributeur : Marie-Claude Arnaud <>
Soumis le : mercredi 17 septembre 2014 - 21:18:54
Dernière modification le : lundi 20 mars 2017 - 13:45:59
Document(s) archivé(s) le : jeudi 18 décembre 2014 - 12:01:43

Fichiers

TwistMaps dimsup.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01065120, version 1
  • ARXIV : 1409.5203

Collections

Citation

Marie-Claude Arnaud. Lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions. Communications in Mathematical Physics, Springer Verlag, 2016, 343 (3), pp.783-810. 〈hal-01065120〉

Partager

Métriques

Consultations de
la notice

200

Téléchargements du document

223