Generalized Nonuniform Dichotomies and Local Stable Manifolds
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We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform dichotomy for the evolution operator that contains the nonuniform exponential and polynomial dichotomies as a very particular case. The family of dichotomies considered allow situations for which the classical Lyapunov exponents are zero. Additionally, we give new examples of application of our stable manifold theorem and study the behavior of the dynamics under perturbations.
KeywordsInvariant manifolds Nonautonomous differential equations Nonuniform generalized dichotomies
Mathematics Subject Classification (2000)37D10 34D09 37D25
This work was partially supported by FCT though Centro de Matemática da Universidade da Beira Interior (project PEst-OE/MAT/UI0212/2011).
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