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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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