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Título: Pullback, forward and chaotic dynamics in 1d nonautonomous linear-dissipative equations
Autor: Caraballo, Tomás
Langa, José
Obaya, Rafael
Año del Documento: 2017
Editorial: IOPPublishing
Descripción: Producción Científica
Documento Fuente: Nonlinearity 30 (2017), no.1, 274-299
Resumen: The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The continuity of the cocycle attractor in the parameter is usually a difficult question. In this paper we develop in detail a 1D non-autonomous linear differential equation and show the richness of non-autonomous dynamics by focusing on the continuity, characterization and chaotic dynamics of the cocycle attractors. In particular, we analyse the sets of continuity and discontinuity for the parameter of the attractors, and relate them with the eventually forward behaviour of the processes. We will also find chaotic behaviour on the attractors in the Li–Yorke and Auslander–Yorke senses. Note that they hold for linear 1D equations, which shows a crucial difference with respect to the presence of chaotic dynamics in autonomous systems.
ISSN: 951-7715
Revisión por Pares: SI
DOI: 10.1088/1361-6544/30/1/274
Patrocinador: info:eu-repo/grantAgreement/EC/H2020/643073
Patrocinador: MINECO/FEDER MTM2015- 66330-P
Version del Editor: http://iopscience.iop.org/issue/0951-7715/30/1
Idioma: eng
URI: http://uvadoc.uva.es/handle/10324/25748
Derechos: info:eu-repo/semantics/openAccess
Aparece en las colecciones:Documentos OpenAire(Open Access Infrastructure for Research in Europe)
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