Omega-limit sets close to singular-hyperbolic attractors

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dc.creatorCarballo, C. M.
dc.creatorMorales, C. A.
dc.date2003-07-23
dc.date.accessioned2026-07-07T04:59:52Z
dc.date.available2026-07-07T04:59:52Z
dc.descriptionWe study the omega-limit sets $ω_X(x)$ 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:ω_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 \cite{gw} and the example in \cite{mpu}.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0307316
dc.identifierhttp://arxiv.org/abs/math/0307316
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68158
dc.subjectDynamical Systems
dc.subjectPrimary 37D30, Secondary 37B25
dc.titleOmega-limit sets close to singular-hyperbolic attractors
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