| Texto completo | |
| Autor(es): |
Carvalho, A. N.
;
Langa, J. A.
;
Moura, R. O.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF NONLINEAR SCIENCE; v. 35, n. 4, p. 35-pg., 2025-08-01. |
| Resumo | |
The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in the literature, we do not require the symbol space to have finite box-counting dimension. Instead, we ask a condition on the semi-continuity of pullback attractors of the system as time goes to infinity. This semi-continuity can be achieved if we suppose the existence of finite-dimensional exponential uniform attractors for the limit symbols, that is, the symbols associated with the asymptotic vector fields of the non-autonomous differential equation. After showing these new results, we apply them to study the box-counting dimension of the uniform attractor for a non-autonomous reaction-diffusion equation, and we find a class of forcing terms for this equation such that their associated symbol spaces have infinite box-counting dimension, but the uniform attractors of the dynamical systems generated by these forcing terms have finite box-counting dimension anyway. (AU) | |
| Processo FAPESP: | 23/11798-5 - Dimensão dos atratores associados a sistemas dinâmicos autônomos e não-autônomos |
| Beneficiário: | Rafael de Oliveira Moura |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |
| Processo FAPESP: | 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação |
| Beneficiário: | Alexandre Nolasco de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/04886-2 - Dimensão dos atratores associados a sistemas dinâmicos autônomos e não-autônomos |
| Beneficiário: | Rafael de Oliveira Moura |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |