Resumen
We prove that if a symplectic diffeomorphism is not partially hyperbolic, then with an arbitrarily small C 1 perturbation we can create a totally elliptic periodic point inside any given open set. As a consequence, a C 1-generic symplectic diffeomorphism is either partially hyperbolic or it has dense elliptic periodic points. This extends the similar results of S. Newhouse in dimension 2 and M.-C. Arnaud in dimension 4. Another interesting consequence is that stably ergodic symplectic diffeomorphisms must be partially hyperbolic, a converse to Shub-Pugh's stable ergodicity conjecture for the symplectic case.
Idioma original | Inglés |
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Páginas (desde-hasta) | 5119-5136 |
Número de páginas | 18 |
Publicación | Transactions of the American Mathematical Society |
Volumen | 358 |
N.º | 11 |
DOI | |
Estado | Publicada - nov. 2006 |
Publicado de forma externa | Sí |