Singular-hyperbolic attractors are chaotic

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dc.creatorAraujo, Vitor
dc.creatorPacifico, Maria Jose
dc.creatorPujals, Enrique
dc.creatorViana, Marcelo
dc.date2005-11-14
dc.date2007-03-22
dc.date.accessioned2026-07-07T12:33:15Z
dc.date.available2026-07-07T12:33:15Z
dc.descriptionWe prove that a singular-hyperbolic 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 Lebesgue (volume) measure subset of the topological basin of attraction. Moreover this measure has absolutely continuous conditional measures along the center-unstable direction, is a $u$-Gibbs state and an equilibrium state for the logarithm of the Jacobian of the time one map of the flow along the strong-unstable direction. This extends to the class of singular-hyperbolic attractors the main elements of the ergodic theory of uniformly hyperbolic (or Axiom A) attractors for flows.
dc.description55 pages, extra figures (now a total of 16), major rearrangement of sections and corrected proofs, improved introduction
dc.identifierhttps://arxiv.org/abs/math/0511352
dc.identifierhttp://arxiv.org/abs/math/0511352
dc.identifierTransactions of the American Mathematical Society, 361 (2009), 2431-2485
dc.identifierdoi:10.1090/S0002-9947-08-04595-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217060
dc.subjectDynamical Systems
dc.subject37C10, 37C40, 37D30
dc.titleSingular-hyperbolic attractors are chaotic
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