| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Ecole Normale Super, DMA, UMR CNRS 8553, F-75005 Paris - France
[2] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen - Denmark
[3] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE; v. 45, n. 6, p. 861-926, NOV-DEC 2012. |
| Web of Science Citations: | 9 |
| Abstract | |
We consider C-2 families t -> of C-4 unimodal maps ft whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure mu(t) of ft depends differentiably on t, as a distribution of order 1. The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of eat for a Benedicks-Carleson map ft, in terms of a single smooth function and the inverse branches of ft along the postcritical orbit. Along the way, we prove that the twisted cohomological equation nu = alpha o f - f' has a continuous solution alpha, if f is Benedicks-Carleson and nu is horizontal for f. (AU) | |
| FAPESP's process: | 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems |
| Grantee: | Jorge Manuel Sotomayor Tello |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 10/08654-1 - Spectral properties of the renormalization operator |
| Grantee: | Daniel Smania Brandão |
| Support Opportunities: | Regular Research Grants |