Analytic invariant manifolds for nonautonomous equations

Luis Barreira, Claudià Valls

DOI: http://dx.doi.org/10.12775/TMNA.2015.035

Abstract


We construct real analytic stable invariant manifolds for sufficiently small perturbations of a linear equation $v'=A(t)v$ admitting a~nonuniform exponential dichotomy. As a byproduct of our approach we obtain an exponential control not only of the trajectories on the invariant manifolds, but also of all their derivatives.

Keywords


Analytic invariant manifolds; nonuniform hyperbolicity

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