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Vanishing asymptotic Maslov index for conformally symplectic flows

Arnaud, Marie-Claude; Florio, Anna; Roos, Valentine (2022), Vanishing asymptotic Maslov index for conformally symplectic flows. https://basepub.dauphine.psl.eu/handle/123456789/23100

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
43
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Author(s)
Arnaud, Marie-Claude
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Florio, Anna
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Roos, Valentine
Ecole normale supérieure de Lyon [Ens Lyon]
Abstract (EN)
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.
Subjects / Keywords
Maslov index; Conformally symplectic flows; twist condition