Nonuniform $(\mu,\nu)$-dichotomies and local dynamics of difference equations
Dynamical Systems
2011-05-12 v1
Abstract
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. We note that we consider situations were 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.
Keywords
Cite
@article{arxiv.1105.2271,
title = {Nonuniform $(\mu,\nu)$-dichotomies and local dynamics of difference equations},
author = {António J. G. Bento and César M. Silva},
journal= {arXiv preprint arXiv:1105.2271},
year = {2011}
}