Strange attractors in saddle-node cycles: Prevalence and globality

• Type: Article in International Scientific Journal
• Date: 1996

Authors

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

Journal

Title: Inventiones Mathematicae

Vol. 125

Pages: 37-74

ISSN: 0020-9910

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 44 Citations

Scopus - 45 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-EBM

DOI: 10.1007/s002220050068

Abstract (EN): We consider parametrized families of diffeomorphisms bifurcating through the creation of critical saddle-node cycles. We show that they always exhibit Henon-like strange attractors for a set of parameter values with positive Lebesgue density at the bifurcation value. Zn open classes of such families the strange attractors are of global type: their basins contain an a priori defined neighbourhood of the cycle. Furthermore, the bifurcation parameter may also be a point of positive density of hyperbolic dynamics.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 38