Nous étudions les variétés invariantes des systèmes dynamiques conformes symplectiques sur une variété symplectique de dimension . Nous montrons d’abord qu’une variété invariante est -isotrope, à supposer que l’entropie de la dynamique restreinte soit petite par rapport au taux de conformalité. Ensuite, quand est exacte et isotrope, nous montrons que est exacte pour un certain choix de primitive de , sous la condition que la dynamique agit trivialement sur la cohomologie de degré de . La conclusion se généralise partiellement si une demi-orbite de est d’adhérence compacte. Enfin, nous décrivons des conditions montrant l’unicité de .
We study invariant manifolds of conformal symplectic dynamical systems on a symplectic manifold of dimension . We first prove the -isotropy of an invariant manifold , assuming the entropy of is small with respect to the conformality rate. Next, when is exact and is isotropic, we show that must be exact for some choice of the primitive of , under the condition that the dynamics acts trivially on the cohomology of degree of . The conclusion partially extends if a one-sided orbit of has compact closure. We eventually describe some conditions showing the uniqueness of .
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@article{JEP_2024__11__159_0,
author = {Marie-Claude Arnaud and Jacques Fejoz},
title = {Invariant submanifolds of conformal symplectic dynamics},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {159--185},
publisher = {\'Ecole polytechnique},
volume = {11},
year = {2024},
doi = {10.5802/jep.252},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.252/}
}
TY - JOUR AU - Marie-Claude Arnaud AU - Jacques Fejoz TI - Invariant submanifolds of conformal symplectic dynamics JO - Journal de l’École polytechnique — Mathématiques PY - 2024 SP - 159 EP - 185 VL - 11 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.252/ DO - 10.5802/jep.252 LA - en ID - JEP_2024__11__159_0 ER -
%0 Journal Article %A Marie-Claude Arnaud %A Jacques Fejoz %T Invariant submanifolds of conformal symplectic dynamics %J Journal de l’École polytechnique — Mathématiques %D 2024 %P 159-185 %V 11 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.252/ %R 10.5802/jep.252 %G en %F JEP_2024__11__159_0
Marie-Claude Arnaud; Jacques Fejoz. Invariant submanifolds of conformal symplectic dynamics. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 159-185. doi : 10.5802/jep.252. https://jep.centre-mersenne.org/articles/10.5802/jep.252/
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