Center manifolds for difference equations—smooth parameter dependence |
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Authors: | Luis Barreira Claudia Valls |
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Institution: | Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal |
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Abstract: | For sufficiently small C1 perturbations of (nonautonomous) linear difference equations with a nonuniform exponential trichotomy, we establish the existence of center manifolds with the optimal C1 regularity. We also consider the case of parameter-dependent perturbations and we obtain the C1 dependence of the center manifolds on the parameter. In addition, we consider arbitrary growth rates with the usual exponential estimates of the form in the notion of exponential trichotomy replaced by where ρ is now an arbitrary function. The proof of the regularity, both of the center manifold and of its dependence, on the parameter is based on the fiber contraction principle. The most technical part of the argument concerns the continuity of the fiber contraction that essentially needs a direct argument. |
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Keywords: | Primary 37D10 37D25 |
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