TAME DYNAMICS AND ROBUST TRANSITIVITY CHAIN-RECURRENCE CLASSES VERSUS HOMOCLINIC CLASSES
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Titre | TAME DYNAMICS AND ROBUST TRANSITIVITY CHAIN-RECURRENCE CLASSES VERSUS HOMOCLINIC CLASSES |
Type de publication | Journal Article |
Year of Publication | 2014 |
Auteurs | Bonatti C., Crovisier S., Gourmelon N., Potrie R. |
Journal | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY |
Volume | 366 |
Pagination | PII S0002-9947(2014)06261-2 |
Date Published | SEP |
Type of Article | Article |
ISSN | 0002-9947 |
Résumé | One main task of smooth dynamical systems consists in finding a good decomposition into elementary pieces of the dynamics. This paper contributes to the study of chain-recurrence classes. It is known that C-1-generically, each chain-recurrence class containing a periodic orbit is equal to the homoclinic class of this orbit. Our result implies that in general this property is fragile. We build a C-1-open set U of tame diffeomorphisms (their dynamics only splits into finitely many chain-recurrence classes) such that for any diffeomorphism in a C-infinity-dense subset of U, one of the chain-recurrence classes is not transitive (and has an isolated point). Moreover, these dynamics are obtained among partially hyperbolic systems with one-dimensional center. |
DOI | 10.1090/S0002-9947-2014-06261-2 |