A C^1 -Generic dichotomy for diffeomorphisms
| dc.creator | Bonatti, C. | |
| dc.creator | Diaz, L. J. | |
| dc.creator | Pujals, E. R. | |
| dc.date | 2006-10-17 | |
| dc.date.accessioned | 2026-07-07T07:29:09Z | |
| dc.date.available | 2026-07-07T07:29:09Z | |
| dc.description | We show that, for every compact n-dimensional manifold, n\geq 1, there is a residual subset of Diff^1(M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of hyperbolicity called dominated splitting (this is a generalization of a bidimensional result of Mane [Ma3}). In particular, we show that any C^1 -robustly transitive diffeomorphism admits a dominated splitting. | |
| dc.description | 64 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0610527 | |
| dc.identifier | http://arxiv.org/abs/math/0610527 | |
| dc.identifier | Ann. of Math. (2), vol. 158 (2003), no.2, 355--418 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117996 | |
| dc.subject | Dynamical Systems | |
| dc.title | A C^1 -Generic dichotomy for diffeomorphisms | |
| dc.type | text |