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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.
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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 : Tuesday, January 14, 2020 - 10:38:15 AM
Long-term archiving on: : Thursday, December 18, 2014 - 12:01:43 PM

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

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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⟩

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