Abstract
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].
Citation
C. M. Carballo. C. A. Morales. "Omega-limit sets close to singular-hyperbolic attractors." Illinois J. Math. 48 (2) 645 - 663, Summer 2004. https://doi.org/10.1215/ijm/1258138404
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