[Coexistence de comportements chaotiques et elliptiques parmi les symplectomorphismes analytiques de toute surface]
Nous montrons la coexistence de comportements chaotique (entropie métrique positive) et elliptique (îlots elliptiques intégrables) parmi les difféomorphismes analytiques symplectiques dans de nombreuses classes d’isotopies et toute surface fermée. En particulier nous résolvons un problème introduit par F. Przytycki (1982).
We show the coexistence of chaotic behaviors (positive metric entropy) and elliptic behaviors (integrable elliptic islands) among analytic, symplectic diffeomorphisms in many isotopy classes of any closed surface. In particular this solves a problem introduced by F. Przytycki (1982).
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Keywords: Symplectomorphism, analytic, positive metric entropy, integrable system, elliptic island, stochastic island, coexistence
Mot clés : Symplectomorphisme, analytique, entropie métrique positive, système integrable, îlot elliptique, îlot stochastique, coexistence
Pierre Berger 1
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@article{JEP_2023__10__525_0,
author = {Pierre Berger},
title = {Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {525--547},
publisher = {\'Ecole polytechnique},
volume = {10},
year = {2023},
doi = {10.5802/jep.224},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.224/}
}
TY - JOUR AU - Pierre Berger TI - Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 525 EP - 547 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.224/ DO - 10.5802/jep.224 LA - en ID - JEP_2023__10__525_0 ER -
%0 Journal Article %A Pierre Berger %T Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 525-547 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.224/ %R 10.5802/jep.224 %G en %F JEP_2023__10__525_0
Pierre Berger. Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface. Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 525-547. doi : 10.5802/jep.224. https://jep.centre-mersenne.org/articles/10.5802/jep.224/
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