engleski

Tempered exponential dichotomies: admissibility and stability under perturbations

We give a characterization of the notion of a tempered ex- ponential dichotomy on a Banach space in terms of an admissibility property. We note that for a linear cocycle over a measure- preserving transformation satisfying a certain integrability assumption, it follows from the Multiplicative ergodic theorem that the dynamics admits a tempered exponential dichotomy if and only if all Lyapunov exponents are nonzero almost everywhere. As a consequence of our approach, we give a new proof of the robustness property of the notion of a tempered exponential dichotomy under suciently small linear perturbations and we establish a version of the Grobman{; ; ; ; ; ; Hartman theorem yielding the existence of topological conjugacies between a linear dynamics with a tempered exponential dichotomy and any suciently small nonlinear perturbation. In addition, we show that the conjugacy maps vary con- tinuously with the perturbation

tempered exponential dichotomies ; robustness ; conjugacies.

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