An estimate on the fractal dimension of attractors of gradient-like dynamical systems

Autor(es)

Bortolan, M. C. ^[1] ; Caraballo, T. ^[2] ; Carvalho, A. N. ^[1] ; Langa, J. A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Seville, Fac Matemat, Dpto Ecuac Diferenciales & Anal Numer, E-41080 Seville - Spain

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 75, n. 14, p. 5702-5722, SEP 2012.
• Citações Web of Science: 0

Resumo

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A{*}) is an attractor-repeller pair for the attractor A of a semigroup [T(t) : t >= 0], then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A{*}, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved. (AU)

• Processo FAPESP: 10/50690-5 - Estimativas da dimensao fractal para atratores globais em semigrupos gradient-like generalizados
• Beneficiário: Matheus Cheque Bortolan
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 08/53094-4 - Sistemas dinâmicos em espaços de dimensão infinita sob perturbações
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Bolsas no Exterior - Pesquisa