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The stability of attractors for non-autonomous perturbations of gradient-like systems

 

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dc.creator Langa Rosado, José Antonio es
dc.creator Robinson, James C. es
dc.creator Suárez Fernández, Antonio es
dc.creator Vidal López, Alejandro es
dc.date.accessioned 2016-10-05T07:26:13Z
dc.date.available 2016-10-05T07:26:13Z
dc.date.issued 2007-03-15
dc.identifier.citation Langa Rosado, J.A., Robinson, J.C., Suárez Fernández, A. y Vidal López, A. (2007). The stability of attractors for non-autonomous perturbations of gradient-like systems. Journal of Differential Equations, 234 (2), 607-625.
dc.identifier.issn 0022-0396 es
dc.identifier.uri http://hdl.handle.net/11441/46955
dc.description.abstract We study the stability of attractors under non-autonomous perturbations that are uniformly small in time. While in general the pullback attractors for the nonautonomous problems converge towards the autonomous attractor only in the Hausdorff semi-distance (upper semicontinuity), the assumption that the autonomous attractor has a ‘gradient-like’ structure (the union of the unstable manifolds of a finite number of hyperbolic equilibria) implies convergence (i.e. also lower semicontinuity) provided that the local unstable manifolds perturb continuously. We go further when the underlying autonomous system is itself gradient-like, and show that all trajectories converge to one of the hyperbolic trajectories as t → ∞. In finite-dimensional systems, in which we can reverse time and apply similar arguments to deduce that all bounded orbits converge to a hyperbolic trajectory as t → −∞, this implies that the ‘gradient-like’ structure of the attractor is also preserved under small non-autonomous perturbations: the pullback attractor is given as the union of the unstable manifolds of a finite number of hyperbolic trajectories. es
dc.description.sponsorship Dirección General de Investigación Científica y Técnica es
dc.description.sponsorship Royal Society es
dc.description.sponsorship Dirección General de Enseñanza Superior es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Elsevier es
dc.relation.ispartof Journal of Differential Equations, 234 (2), 607-625.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ *
dc.title The stability of attractors for non-autonomous perturbations of gradient-like systems es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/submittedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico es
dc.relation.projectID MTM2005-01412 es
dc.relation.projectID BFM2003-06446 es
dc.relation.projectID MTM2006-07932 es
dc.relation.projectID BFM2003-03810 es
dc.relation.publisherversion http://ac.els-cdn.com/S0022039606004694/1-s2.0-S0022039606004694-main.pdf?_tid=308046f6-8acc-11e6-96bc-00000aab0f6b&acdnat=1475652207_32b2fffae1a6c87a066593b6e0f44e24 es
dc.identifier.doi 10.1016/j.jde.2006.11.016 es
dc.contributor.group Universidad de Sevilla. FQM314: Análisis Estocástico de Sistemas Diferenciales es
dc.contributor.group Universidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Software es
idus.format.extent 22 p. es
dc.journaltitle Journal of Differential Equations es
dc.publication.volumen 234 es
dc.publication.issue 2 es
dc.publication.initialPage 607 es
dc.publication.endPage 625 es
dc.identifier.idus https://idus.us.es/xmlui/handle/11441/46955
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