2 3 Ju l 2 00 3 OMEGA - LIMIT SETS CLOSE TO SINGULAR - HYPERBOLIC ATTRACTORS
نویسنده
چکیده
We 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 ∈ U : ω Y (x) contains a singularity} is 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].
منابع مشابه
Omega-limit Sets Close to Singular-hyperbolic Attractors
We study the omega-limit sets ωX(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 ∈ U : ωY (x) contains a singularity} is 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 ...
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