Abstract
In this work we show if a linear nonautonomous system of ordinary differential equations satisfies a bounded growth condition, then it is exponentially expansive (a slightly stronger condition than uniformly noncritical as defined by Massera and Schaffer) on a half-line if and only if it has an exponential dichotomy and on a whole line if and only if it has an exponential dichotomy on both half-lines and no nontrivial bounded solution. We relate these theorems to Sacker and Sell’s work on linear skew-product flows and also examine the robustness of exponential expansivity under perturbation.
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