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 |
dcterms.identifier | https://ror.org/03yxnpp24 | |
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 | |