Work

Vanishing asymptotic Maslov index for conformally symplectic flows

Year: 2024

Type: article

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.

Source: Annales Henri Lebesgue

DOI: 10.5802/ahl.202

Authors: Marie-Claude Arnaud, Anna Florio, Valentine Roos

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: Conformally symplectic dynamics, beyond symplectic dynamics

OpenAlex ID: W4402270135

FWCI: 0.65

Cites: 33

Cited by: 1

Related to: 10