| Full text | |
| Author(s): |
Carvalho, A. N.
;
Langa, J. A.
;
Moura, R. O.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF NONLINEAR SCIENCE; v. 35, n. 4, p. 35-pg., 2025-08-01. |
| Abstract | |
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) | |
| FAPESP's process: | 23/11798-5 - Dimension of the attractors associated to autonomous and nonautonomous dynamical systems |
| Grantee: | Rafael de Oliveira Moura |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 20/14075-6 - Dynamical systems and their attractors under perturbations |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/04886-2 - Dimension of the attractors associated to autonomous and nonautonomous dynamical systems |
| Grantee: | Rafael de Oliveira Moura |
| Support Opportunities: | Scholarships in Brazil - Doctorate |