Center manifolds and optimal estimates
Let \((A_n)_{n\in\mathbb{Z}}\) be a family of invertible bounded linear operators on a Banach space \(X\) and consider the \(C^k\) maps \(f_n:X\to X\), \(n\in\mathbb{Z}\), with certain conditions such that \(F_n=A_n+f_n\) is invertible. The aim of the paper is to prove the existence of center manifolds for the dynamics \[ v_{n+1}=F_n (v_n),\; n\in\mathbb{Z}. \] The authors consider the general case of a discrete nonautonomous dynamics with nonuniform exponential trichotomy.
scientific article; zbMATH DE number 6305044