American Institute of Mathematical Sciences

April  2011, 30(1): 55-76. doi: 10.3934/dcds.2011.30.55

Regularity of center manifolds under nonuniform hyperbolicity

 1 Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa 2 Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa

Received  December 2009 Revised  May 2010 Published  February 2011

We construct $C^k$ invariant center manifolds for differential equations $u'=A(t)u+f(t,u)$ obtained from sufficiently small perturbations of a nonuniform exponential trichotomy. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. In addition, we can also consider linear perturbations with the same method.
Citation: Luis Barreira, Claudia Valls. Regularity of center manifolds under nonuniform hyperbolicity. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 55-76. doi: 10.3934/dcds.2011.30.55
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References:
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