We study the omega-limit sets $\omega_X(x)$ in an isolating block $U$
of a singular-hyperbolic attractor
for three-dimensional vector fields $X$.
We prove that for every
vector field $Y$ close to $X$
the set $
\{x\in U:\omega_Y(x)$ contains a singularity$\}$
is {\em residual} in $U$.
This is used to prove the persistence of
singular-hyperbolic attractors
with only one singularity
as chain-transitive Lyapunov stable sets.
These results generalize well known properties of the
geometric Lorenz attractor [GW]
and the example in [MPu].
Publié le : 2004-04-15
Classification:
37D05,
37B99,
37C20,
37C70
@article{1258138404,
author = {Carballo, C. M. and Morales, C. A.},
title = {Omega-limit sets close to singular-hyperbolic attractors},
journal = {Illinois J. Math.},
volume = {48},
number = {3},
year = {2004},
pages = { 645-663},
language = {en},
url = {http://dml.mathdoc.fr/item/1258138404}
}
Carballo, C. M.; Morales, C. A. Omega-limit sets close to singular-hyperbolic attractors. Illinois J. Math., Tome 48 (2004) no. 3, pp. 645-663. http://gdmltest.u-ga.fr/item/1258138404/