Singular-hyperbolic attractors are chaotic
نویسندگان
چکیده
منابع مشابه
4 N ov 2 00 5 SINGULAR - HYPERBOLIC ATTRACTORS ARE CHAOTIC
We prove that a singular-hyperbolic (or Lorenz-like) attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their orbits coincide. Secondly, there exists a physical (or Sinai-Ruelle-Bowen) measure supported on the attractor whose ergodic basin covers a full...
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An attractor is a transitive set of a flow to which all positive orbit close to it converges. An attractor is singular-hyperbolic if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction [16]. The geometric Lorenz attractor [6] is an example of a singular-hyperbolic attractor with topological dimension ≥ 2. We shall prove that all singular-hyp...
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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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-08-04595-9