Exponential trichotomies and continuity of invariant manifolds

Autores

  • Severino Horácio da Silva Universidade Federal de Campina Grande UAME/CCT/UFCG.
  • Antonio Luiz Pereira Instituto de Matemática e Estatística, Universidade de São Paulo IME/USP

DOI:

https://doi.org/10.11606/issn.2316-9028.v5i2p111-134

Resumo

In this work, we consider the invariant manifolds for the family of equations

x  = Ax + f(", x), where A the is generator of a strongly continuous semigroup of linear operators in a Banach space X and f(", ·) : X ! X is continuous. The existence of stable (unstable) and center-stable (center-unstable) manifolds for a large class of these equations has been proved in [2]. We prove here that, if A admits a exponential trichotomy and f satisfies some suitable regularity hypotheses, then those manifolds are continuous with respect to the parameter".

 

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Biografia do Autor

  • Severino Horácio da Silva, Universidade Federal de Campina Grande UAME/CCT/UFCG.
    Unidade Acadêmica de Matemática e Estatística da Universidade Federal de Campina Grande UAME/CCT/UFCG.

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Publicado

2011-12-30

Edição

Seção

Artigos

Como Citar

Exponential trichotomies and continuity of invariant manifolds. (2011). São Paulo Journal of Mathematical Sciences, 5(2), 111-134. https://doi.org/10.11606/issn.2316-9028.v5i2p111-134