Nonuniform behavior and robustness |
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Authors: | L Barreira C Silva C Valls |
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Institution: | a Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal b Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal |
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Abstract: | We establish the robustness of linear cocycles in Banach spaces admitting a nonuniform exponential dichotomy. We first obtain robustness results for positive and negative time, by establishing exponential behavior along certain subspaces, and showing that the associated sequences of projections have bounded exponential growth. We then establish a robustness result in Z by constructing explicitly appropriate projections on the stable and unstable subspaces. We emphasize that in general these projections may be different from those obtained separately from the robustness for positive and negative time. We also consider the case of strong nonuniform exponential dichotomies. |
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Keywords: | 34D09 34D10 37D99 |
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