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Nonuniform (μ,ν)-dichotomies and stable manifolds for nonautonomous equations
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Abstract:
In this talk we will obtain stable manifold theorems for perturbations of nonautonomous linear difference and differential equations possessing a very general type of nonuniform dichotomy that we call nonuniform (\mu, \nu)-dichotomy (\mu and \nu correspond to the rates of growth allowed for the uniform and nonuniform parts of the dichotomy). We note that our setting allows us to obtain stable manifolds in situations where the classical Lyapunov exponents are zero. Additionally, we study the behavior of the manifolds under perturbations. |
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