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Nonuniform \((\mu, \nu)\)-dichotomies and local dynamics of difference equations. (English) Zbl 1225.37036

Summary: We obtain a local stable manifold theorem for perturbations of nonautonomous linear difference equations possessing a very general type of nonuniform dichotomy, possibly with different growth rates in the uniform and nonuniform parts. Note that we consider situations where the classical Lyapunov exponents can be zero. Additionally, we study how the manifolds decay along the orbit of a point as well as the behavior under perturbations and give examples of nonautonomous linear difference equations that admit the dichotomies considered.

MSC:

37D10 Invariant manifold theory for dynamical systems
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations
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