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Título
Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time
Año del Documento
2025
Editorial
Elsevier
Descripción
Producción Científica
Documento Fuente
Journal of Differential Equations 2025, vol. 414, p. 609–644.
Resumen
New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast
time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate boundedness of the solutions of the layer problems, inflated pullback attractors are considered. In general, one cannot disregard the inflated version of the pullback attractor, but it is possible under the continuity of the fiber projection map of the attractor. The problem of the limit of the solutions of the slow-fast system at each fixed positive value of the slow time is also treated and in this formulation the critical set is given by the union of the fibers of the pullback attractors. The results can be seen as extensions of the classical Tikhonov theorem to the nonautonomous setting.
Palabras Clave
Singularly perturbed ODEs; Nonautonomous fast dynamics; Skew-product semiflows; Nonautonomous attractors
ISSN
0022-0396
Revisión por pares
SI
Patrocinador
Este trabajo forma parte de los proyectos de investigación: MICIIN/FEDER Grant PID2021-125446NB-I00, Universidad de Valladolid Grant PIP-TCESC-2020, y UKRI Grant EP/X027651/1.
Idioma
eng
Tipo de versión
info:eu-repo/semantics/acceptedVersion
Derechos
openAccess
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