Solution of the basin problem for Henon-like attractors

Authors
Benedicks, M Viana, M
Citation
M. Benedicks et M. Viana, Solution of the basin problem for Henon-like attractors, INVENT MATH, 143(2), 2001, pp. 375-434
Citations number
23
Categorie Soggetti
Mathematics
Journal title
INVENTIONES MATHEMATICAE
ISSN journal
00209910 → ACNP
Volume
143
Issue
2
Year of publication
2001
Pages
375 - 434
Database
ISI
SICI code
0020-9910(200102)143:2<375:SOTBPF>2.0.ZU;2-W
Abstract
For a large class of non-uniformly hyperbolic attractors of dissipative dif feomorphisms, we prove that there are no "holes" in the basin of attraction : stable manifolds of points in the attractor fill-in a full Lebesgue measu re subset. Then, Lebesgue almost every point in the basin is generic for th e SRB (Sinai-Ruelle-Bowen) measure of the attractor. This solves a problem posed by Sinai and by Ruelle, for this class of systems.