A generic $C^1$ map has no absolutely continuous invariant probability measure
| dc.creator | Avila, Artur | |
| dc.creator | Bochi, Jairo | |
| dc.date | 2006-05-29 | |
| dc.date | 2006-10-18 | |
| dc.date.accessioned | 2026-07-07T07:14:36Z | |
| dc.date.available | 2026-07-07T07:14:36Z | |
| dc.description | Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \ge 1$. We consider the set of $C^1$ maps $f:M\to M$ which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual (dense $G_δ) set in the $C^1$ topology. In the course of the proof, we need a generalization of the usual Rokhlin tower lemma to non-invariant measures. That result may be of independent interest. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605729 | |
| dc.identifier | http://arxiv.org/abs/math/0605729 | |
| dc.identifier | Nonlinearity 19 (2006) 2717-2725 | |
| dc.identifier | doi:10.1088/0951-7715/19/11/001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112944 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C40 | |
| dc.title | A generic $C^1$ map has no absolutely continuous invariant probability measure | |
| dc.type | text |