RT info:eu-repo/semantics/article
T1 Tracking nonautonomous attractors in singularly perturbed systems of ODEs with dependence on the fast time
A1 Longo, Iacopo P.
A1 Obaya, Rafael
A1 Sanz Gil, Ana María
A1 Sanz
K1 Singularly perturbed ODEs; Nonautonomous fast dynamics; Skew-product semiflows; Nonautonomous  attractors
AB 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.
PB Elsevier
SN 0022-0396
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/69913
UL https://uvadoc.uva.es/handle/10324/69913
LA eng
NO Journal of Differential Equations  2025, vol. 414, p. 609–644.
NO Producción Científica
DS UVaDOC
RD 23-nov-2024