Artículo
Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
Autor/es | Wang, Yejuan
Caraballo Garrido, Tomás |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2020-08 |
Fecha de depósito | 2020-09-08 |
Publicado en |
|
Resumen | In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition
are equivalent. Next, the stability of gradient-like general dynamical systems ... In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems is analyzed. In particular, we show that a gradient-like general dynamical system is stable under perturbations, and that Morse sets are upper semicontinuous with respect to perturbations. Moreover, we prove that any solution of perturbed general dynamical systems should be close to some Morse set of the unperturbed gradient-like general dynamical system. We do not assume local compactness for the metric phase space X, unlike previous results in the literature. Finally, we extend the Morse decomposition theory of single-valued nonautonomous dynamical systems to the multi-valued case, without imposing any compactness of the parameter spaces. |
Agencias financiadoras | National Natural Science Foundation of China Fundamental Research Funds for the Central Universities Ministerio de Economía y Competitividad (MINECO). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Junta de Andalucía. Consejería de Innovación Ciencia y Empresa |
Identificador del proyecto | 41875084
11571153 lzujbky-2018-it58 lzujbky-2018-ot03 MTM2015-63723-P P12-FQM-1492 |
Cita | Wang, Y. y Caraballo Garrido, T. (2020). Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems - Series S, 13 (8), 2303-2326. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Morse decomposition for gradie ... | 384.2Kb | [PDF] | Ver/ | |