Invariant manifolds for difference equations with generalized trichotomies

Bento, António J. G. 

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On an arbitrary Banach space, assuming that a linear nonautonomous difference equation \linebreak x_{m+1} = A_m x_m admits a very general type of trichotomy, we establish conditions for the existence of global Lipschitz invariant center manifolds of the perturbed equation x_{m+1} = A_m x_m + f_m(x_m). Our results not only improve results already existing in the literature, but also include new cases.

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Bento, António J. G.