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Input-output conditions for the asymptotic behavior of linear skew-product flows and applications

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  • In this paper we present a new approach concerning the uniform exponential dichotomy of linear skew-product flows and extend existing results on exponential dichotomy roughness for variational systems in infinite dimensional spaces. We introduce new concepts of admissibility and we deduce their connections with the uniform exponential dichotomy of discrete linear skew-product flows. We apply our results at the study of the exponential dichotomy roughness of discrete linear skew-product flows, presenting an estimation for the lower bound of the dichotomy radius.
    Mathematics Subject Classification: Primary: 34D09, Secondary: 39A11, 93D25, 46E30.


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