Topological structure of (partially) hyperbolic sets with positive volume

• Type: Article in International Scientific Journal
• Date: 2008

Authors

alves, jf (Author) FCUP; pinheiro, v (Author) Other

Journal

Title: Transactions of the American Mathematical Society

Vol. 360 No. 12

Pages: 5551-5569

ISSN: 0002-9947

Publisher: American Mathematical Society

Indexing

ISI Web of Knowledge - 12 Citations

Scopus - 15 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-4YE

DOI: 10.1090/s0002-9947-08-04484-x

Abstract (EN): We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is larger than one. We show in particular that there are no partially hyperbolic horseshoes with positive volume for such diffeomorphisms. We also give a description of the limit set of almost every point belonging to a hyperbolic set or a partially hyperbolic set with positive volume.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19