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Flattening, squeezing and the existence of random attractors


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dc.creator Kloeden, Peter E. es
dc.creator Langa Rosado, José Antonio es 2016-05-16T06:35:55Z 2016-05-16T06:35:55Z 2007-01
dc.identifier.citation Kloeden, P.E. y Langa Rosado, J.A. (2007). Flattening, squeezing and the existence of random attractors. Proceedings of the Royal Society : mathematical, 463, 163-181. es
dc.identifier.issn 1364-5021 es
dc.description.abstract The study of qualitative properties of random and stochastic differential equations is now one of the most active fields in the modern theory of dynamical systems. In the deterministic case, the properties of flattening and squeezing in infinite-dimensional autonomous dynamical systems require the existence of a bounded absorbing set and imply the existence of a global attractor. The flattening property involves the behaviour of individual trajectories while the squeezing property involves the difference of trajectories. It is shown here that the flattening property is implied by the squeezing property and is in fact weaker, since the attractor in a system with the flattening property can be infinite-dimensional, whereas it is always finite-dimensional in a system with the squeezing property. The flattening property is then generalized to random dynamical systems, for which it is called the pullback flattening property. It is shown to be weaker than the random squeezing property, but equivalent to pullback asymptotic compactness and pullback limit-set compactness, and thus implies the existence of a random attractor. The results are also valid for deterministic non-utonomous dynamical systems formulated as skew-product flows. es
dc.description.sponsorship Ministerio de Educación y Ciencia es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Royal Society es
dc.relation.ispartof Proceedings of the Royal Society : mathematical, physical and engineering sciences, 463, 163-181 es
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri *
dc.subject flattening es
dc.subject random dynamical systems es
dc.subject random attractors es
dc.subject squeezing property es
dc.title Flattening, squeezing and the existence of random attractors es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/publishedVersion 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 SAB2004-0146 es
dc.identifier.doi es
idus.format.extent 19 p. es
dc.journaltitle Proceedings of the Royal Society : mathematical es
dc.publication.volumen 463 es
dc.publication.initialPage 163 es
dc.publication.endPage 181 es
dc.contributor.funder Ministerio de Educación y Ciencia (MEC). España
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