Conformally symplectic dynamics, beyond symplectic dynamics – CoSyDy
Our project aims to study conformally symplectic dynamics (CSD) which preserve a symplectic structure up to a constant scaling factor, and its generalizations to conformally symplectic manifolds in all its aspects. In particular, • Which conditions on the dynamics and on the manifold imply the existence of an attractor ? • We will investigate various features of these attractors : their invariant measures, their entropy and the distribution of functions that are defined at almost every point (rotation vectors, asymptotic Maslov indices, Lyapunov exponents etc.) • We will use spectral invariants from symplectic geometry to prove existence and uniqueness results for Lagrangian submanifolds in the attractor. • We will explore the dependence of large families of CSD systems on various parameters, e.g. the scaling factor k. It is believed that the dynamics simplifies when k is small, and one may expect that some information on conservative systems can be obtained by letting k tend to 1.
We will prove rigidity results by using variational symplectic techniques.
Madame MARIE-CLAUDE ARNAUD (Institut de mathématiques de Jussieu - Paris Rive Gauche)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
UMPA Unité de mathématiques pures et appliquées de l'ENS de Lyon
IMJ-PRG Institut de mathématiques de Jussieu - Paris Rive Gauche
Help of the ANR 295,670 euros
Beginning and duration of the scientific project: September 2021 - 48 Months