An isolated saddle-node bifurcation occurring inside a horseshoe

Authors
Cao, YL Kiriki, S
Citation
Yl. Cao et S. Kiriki, An isolated saddle-node bifurcation occurring inside a horseshoe, DYN ST SYST, 15(1), 2000, pp. 11-22
Citations number
11
Categorie Soggetti
Mechanical Engineering
Journal title
DYNAMICS AND STABILITY OF SYSTEMS
ISSN journal
02681110 → ACNP
Volume
15
Issue
1
Year of publication
2000
Pages
11 - 22
Database
ISI
SICI code
0268-1110(200003)15:1<11:AISBOI>2.0.ZU;2-H
Abstract
In this paper, we consider a smooth are of diffeomorphisms which has a sadd le-node bifurcation 'inside' a non-trivial invariant set which is a deforma tion of a horseshoe. We show that this saddle-node bifurcation is 'isolated ', that is, hyperbolicity is maintained before and after the saddle-node bi furcation. Moreover, we construct a C-2-open set of arcs having the same pr operty.