SRB measures for partially hyperbolic systems whose central direction is mostly expanding

• Type: Article in International Scientific Journal
• Date: 2000

Authors

alves, jf (Author) FCUP; bonatti, c (Author) Other; viana, m (Author) Other

Journal

Title: Inventiones Mathematicae

Vol. 140

Pages: 351-398

ISSN: 0020-9910

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 222 Citations

Scopus - 221 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-05V

DOI: 10.1007/s002220000057

Abstract (EN): We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms - the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting - under the assumption that the complementary subbundle is non-uniformly expanding, If the rate of expansion (Lyapunov exponents) is bounded away from zero, then there are only finitely many SRB measures. Our techniques extend to other situations, including certain maps with singularities or critical points, as well as diffeomorphisms having only a dominated splitting (and no uniformly hyperbolic subbundle).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 48