On the Hartman-Grobman Theorem with Parameters

Autor(es)

Rodrigues, Hildebrando M. ^[1] ; Sola-Morales, J. ^[2]

Afiliação do(s) autor(es)

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

^[2] Univ Politecn Cataluna, Dept Matemat Aplicada 1, E-08028 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Dynamics and Differential Equations; v. 22, n. 3, p. 473-489, SEP 2010.
• Citações Web of Science: 4

Resumo

The Hartman-Grobman Theorem of linearization is extended to families of dynamical systems in a Banach space X, depending continuously on parameters. We prove that the conjugacy also changes continuously. The cases of nonlinear maps and flows are considered, and both in global and local versions, but global in the parameters. To use a special version of the Banach-Caccioppoli Theorem we introduce equivalent norms on X depending on the parameters. The functional setting is suitable for applications to some nonlinear evolution partial differential equations like the nonlinear beam equation. (AU)

• Processo FAPESP: 03/10042-0 - Sistemas dinâmicos não lineares e aplicações
• Beneficiário: Alexandre Nolasco de Carvalho
• Linha de fomento: Auxílio à Pesquisa - Programa PRONEX - Temático