Coexistence of chaotic and elliptic behaviors among analytic, symplectic diffeomorphisms of any surface
[Coexistence de comportements chaotiques et elliptiques parmi les symplectomorphismes analytiques de toute surface]
Berger, Pierre1
1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS, Sorbonne Université, Université de Paris 4 place Jussieu, 75252 Paris Cedex 05, France
Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 525-547

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).

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).

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.224
Classification : 37J70, 37J46, 37F80, 37E30, 37D45, 37D25
Keywords: Symplectomorphism, analytic, positive metric entropy, integrable system, elliptic island, stochastic island, coexistence
Mots-clés : Symplectomorphisme, analytique, entropie métrique positive, système integrable, îlot elliptique, îlot stochastique, coexistence

Berger, Pierre 1

1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS, Sorbonne Université, Université de Paris 4 place Jussieu, 75252 Paris Cedex 05, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     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},
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Berger, Pierre. 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

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