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dc.creatorBortolan, Matheus Chequees
dc.creatorCaraballo Garrido, Tomás
dc.creatorCarvalho, Alexandre Nolasco
dc.creatorLanga Rosado, José Antonio
dc.description.abstractThis paper is devoted to the investigation of the dynamics of non-autonomous differential equations. The description of the asymptotic dynamics of non-autonomous equations lies on dynamical structures of some associated limiting non-autonomous - and autonomous - differential equations (one for each global solution in the attractor of the driving semigroup of the associated skew product semi-flow). In some cases, we have infinitely many limiting problems (in contrast with the autonomous - or asymptotically autonomous - case for which we have only one limiting problem; that is, the semigroup itself). We concentrate our attention in the study of the Morse decomposition of attractors for these non-autonomous limiting problems as a mean to understand some of the asymptotics of our non-autonomous differential equations. In particular, we derive a Morse decomposition for the global attractors of skew product semiflows (and thus for pullback attractors of non-autonomous differential equations) from a Morse decomposition of the attractor for the associated driving semigroup. Our theory is well suited to describe the asymptotic dynamics of non-autonomous differential equations defined on the whole line or just for positive times, or for differential equations driven by a general semigroup.
dc.relation.ispartofJournal of Differential Equations, 255(8), 2436-2462es
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Españaes
dc.subjectNon-autonomous differential equations
dc.subjectMorse decomposition
dc.titleSkew Product Semiflows and Morse Decompositiones
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numéricoes

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