Robustly transitive sets and heterodimensional cycles

• Type: Article in International Scientific Journal
• Date: 2003

Authors

Bonatti, C (Author) Other; Diaz, LJ (Author) Other; Pujals, ER (Author) Other; Rocha, J (Author) FCUP

Journal

Title: Asterisque

Pages: 187-222

ISSN: 0303-1179

Publisher: Societe Mathematique de France

Indexing

ISI Web of Knowledge - 45 Citations

Scopus - 48 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-J6E

Abstract (EN): It is known that all non-hyperbolic robustly transitive sets Lambda(phi) have a dominated splitting and, generically, contain periodic points of different indices. We show that, for a C-1-dense open subset of diffeomorphisms phi, the indices of periodic points in a robust transitive set Lambda(phi) form an interval in N. We also prove that the homoclinic classes of two periodic points in Lambda(phi) are robustly equal. Finally, we describe what sort of homoclinic tangencies may appear in Lambda(phi) by studying its dominated splittings.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 36