Article
Equi-attraction and continuity of attractors for skew-product semiflows
Author/s | Caraballo Garrido, Tomás
Carvalho, Alexandre Nolasco Barbosa da Costa, Henrique Langa Rosado, José Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2016-11 |
Deposit Date | 2017-01-24 |
Published in |
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Abstract | In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, and equi-attraction and continuity of uniform and cocycle attractors associated to non-autonomous ... In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, and equi-attraction and continuity of uniform and cocycle attractors associated to non-autonomous dynamical systems. To this aim proper notions of equi-attraction have to be introduced in phase spaces where the driving systems depend on a parameter. Results on the upper and lower-semicontinuity of uniform and cocycle attractors are relatively new in the literature, as a deep understanding of the internal structure of these sets is needed, which is generically difficult to obtain. The notion of lifted invariance for uniform attractors allows us to compare the three types of attractors and introduce a common framework in which to study equi-attraction and continuity of attractors. We also include some results on the rate of attraction to the associated attractors. |
Project ID. | 305230/2011-5
238/2011 2008/55516-3 MTM2011-22411 P12-FQM-1492 |
Citation | Caraballo Garrido, T., Carvalho, A.N., Barbosa da Costa, H. y Langa Rosado, J.A. (2016). Equi-attraction and continuity of attractors for skew-product semiflows. Discrete and Continuous Dynamical Systems - Series B, 21 (9), 2949-2967. |
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