Smooth center manifolds for nonuniformly partially hyperbolic trajectories |
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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: | We establish the existence of unique smooth center manifolds for ordinary differential equations v′=A(t)v+f(t,v) in Banach spaces, assuming that v′=A(t)v admits a nonuniform exponential trichotomy. This allows us to show the existence of unique smooth center manifolds for the nonuniformly partially hyperbolic trajectories. In addition, we prove that the center manifolds are as regular as the vector field. Our proof of the Ck smoothness of the manifolds uses a single fixed point problem in an appropriate complete metric space. To the best of our knowledge we establish in this paper the first smooth center manifold theorem in the nonuniform setting. |
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Keywords: | 34D09 37D10 37D25 |
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