Non-critical saddle-node cycles and robust non-hyperbolic dynamics

• Type: Article in International Scientific Journal
• Date: 1997

Authors

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

Journal

Title: Dynamics and Stability of Systems

Vol. 12

Pages: 109-135

ISSN: 0268-1110

Publisher: Oxford University Press

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 5 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

Other information

Authenticus ID: P-001-B9M

DOI: 10.1080/02681119708806240

Abstract (EN): We study arcs of diffeomorphisms (f(t)) in manifolds of dimension greater than or equal to three bifurcating via non-critical saddle-node cycles. We construct an open set S of such arcs for which, after the bifurcation, every diffeomorphism f(t) does not satisfy Axiom A. We also exhibit an open subset S' of S such that after the bifurcation every diffeomorphism has a partially hyperbolic set of saddle-type which is persistent, locally maximal and transitive. As a consequence, we get a submanifold of codimension-1 of diffeomorphisms with a saddle-node that locally separates the set of Morse-Smale systems from the diffeomorphisms with a partially hyperbolic transitive set.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27