کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4592443 | 1335101 | 2009 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Stable invariant manifolds for parabolic dynamics Stable invariant manifolds for parabolic dynamics](/preview/png/4592443.png)
We consider nonautonomous equations v′=A(t)v in a Banach space that exhibit stable and unstable behaviors with respect to arbitrary growth rates ecρ(t) for some function ρ(t). This corresponds to the existence of a “generalized” exponential dichotomy, which is known to be robust. When ρ(t)≠t this behavior can be described as a type of parabolic dynamics. We consider the general case of nonuniform exponential dichotomies, for which the Lyapunov stability is not uniform. We show that for any sufficiently small perturbation f of a “generalized” exponential dichotomy there is a stable invariant manifold for the perturbed equation v′=A(t)v+f(t,v). We also consider the case of exponential contractions, which allow a simpler treatment, and we show that they persist under sufficiently small nonlinear perturbations.
Journal: Journal of Functional Analysis - Volume 257, Issue 4, 15 August 2009, Pages 1018-1029