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Characterization of stable manifolds for nonuniform exponential dichotomies

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  • We establish the existence of smooth stable manifolds for nonautonomous differential equations $v'=A(t)v+f(t,v)$ in a Banach space, obtained from sufficiently small perturbations of a linear equation $v'=A(t)v$ admitting a nonuniform exponential dichotomy. In addition to the exponential decay of the flow on the stable manifold we also obtain the exponential decay of its derivative with respect to the initial condition. Furthermore, we give a characterization of the stable manifold in terms of the exponential growth rate of the solutions.
    Mathematics Subject Classification: Primary: 37D10, 34D99.

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