Singular hyperbolic systems

Authors
Morales, CA Pacifico, MJ Pujals, ER
Citation
Ca. Morales et al., Singular hyperbolic systems, P AM MATH S, 127(11), 1999, pp. 3393-3401
Citations number
12
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
127
Issue
11
Year of publication
1999
Pages
3393 - 3401
Database
ISI
SICI code
0002-9939(199911)127:11<3393:SHS>2.0.ZU;2-L
Abstract
We construct a class of vector fields on 3-manifolds containing the hyperbo lic ones and the geometric Lorenz attractor. Conversely, we shall prove tha t nonhyperbolic systems in this class resemble the Lorenz attractor: they h ave Lorenz-like singularities accumulated by periodic orbits and they canno t be approximated by flows with nonhyperbolic critical elements.