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Vanishing asymptotic Maslov index for conformally symplectic flows

Abstract : Motivated by Mather theory of minimizing measures for symplectic twist dynamics, we study conformally symplectic flows on a cotangent bundle. These dynamics are the most general dynamics for which it makes sense to look at (asymptotic) dynamical Maslov index. Our main result is the existence of invariant measures with vanishing index without any convexity hypothesis, in the general framework of conformally symplectic flows. A degenerate twist-condition hypothesis implies the existence of ergodic invariant measures with zero dynamical Maslov index and thus the existence of points with zero dynamical Maslov index.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03714715
Contributor : Anna Florio Connect in order to contact the contributor
Submitted on : Tuesday, July 5, 2022 - 6:30:48 PM
Last modification on : Friday, August 5, 2022 - 11:59:59 AM

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  • HAL Id : hal-03714715, version 1

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Marie-Claude Arnaud, Anna Florio, Valentine Roos. Vanishing asymptotic Maslov index for conformally symplectic flows. 2022. ⟨hal-03714715⟩

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