Partially hyperbolic and transitive dynamics generated by heteroclinic cycles

• Type: Article in International Scientific Journal
• Date: 2001

Authors

Diaz, LJ (Author) Other; Rocha, J (Author) FCUP

Journal

Title: Ergodic Theory and Dynamical Systems

Vol. 21

Pages: 25-76

ISSN: 0143-3857

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 26 Citations

Scopus - 28 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-WFQ

DOI: 10.1017/s0143385701001067

Abstract (EN): We study C-k-diffeomorphisms, k greater than or equal to 1, f : M --> M, exhibiting hetero-dimensional cycles (i.e, cycles containing periodic points of different stable indices). We prove that if f can not be Ck-approximated by diffeomorphisms with homoclinic tangencies, then f is in the closure of an open set U subset of Diff(k) (M) consisting of diffeomorphisms g with a non-hyperbolic transitive set hg which is locally maximal and strongly partially hyperbolic (the partially hyperbolic splitting at hg has three non-trivial directions). As a consequence, in the case of 3-manifolds, we give new examples of open sets of C-1-diffeomorphisms for which residually infinitely many sinks or sources coexist (C-1-Newhouse's phenomenon). We also prove that the occurrence of non-hyperbolic dynamics has persistent character in the unfolding of heterodimensional cycles.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 52