SADDLE-FOCUS SINGULAR CYCLES AND PREVALENCE OF HYPERBOLICITY

Authors
Citation
B. Sanmartin, SADDLE-FOCUS SINGULAR CYCLES AND PREVALENCE OF HYPERBOLICITY, Annales de l Institut Henri Poincare. Analyse non lineaire, 15(5), 1998, pp. 623-649
Citations number
13
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
02941449
Volume
15
Issue
5
Year of publication
1998
Pages
623 - 649
Database
ISI
SICI code
0294-1449(1998)15:5<623:SSCAPO>2.0.ZU;2-3
Abstract
The objective of this work is to study the 2-parameter unfolding of an intricate bifurcating dynamical structure in dimension 3, namely a sa ddle-focus singular cycle. It is showed that hyperbolicity is a preval ent phenomena: the initial system is a total density point of hyperbol ic dynamics. This dynamic exhibit either simple critical elements or n ontrivial basic set, It seems to be the first time that non-trivial hy perbolicity (as well as its prevalence) is proved for the maximal inva riant set for a perturbation of a vector field with a cycle containing a saddle-focus singularity. (C) Elsevier, Paris.