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.
Document type :
Journal articles
Complete list of metadatas

https://hal-univ-avignon.archives-ouvertes.fr/hal-01065120
Contributor : Marie-Claude Arnaud <>
Submitted on : Wednesday, September 17, 2014 - 9:18:54 PM
Last modification on : Saturday, March 23, 2019 - 1:20:42 AM
Long-term archiving on: Thursday, December 18, 2014 - 12:01:43 PM

Files

TwistMaps dimsup.pdf
Files produced by the author(s)

Identifiers

  • 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⟩

Share

Metrics

Record views

323

Files downloads

326