Nonuniform dichotomic behavior: Lipschitz invariant manifolds for difference equations

TL;DR

This paper establishes the existence of Lipschitz invariant manifolds for perturbed nonautonomous difference equations with general dichotomic behavior, extending previous results to nonhyperbolic cases.

Contribution

It provides new global and local theorems on invariant manifolds under very general dichotomic conditions, including nonhyperbolic scenarios.

Findings

Invariant manifolds exist under broad dichotomic conditions

Results include nonhyperbolic cases

Includes new examples and generalizes previous theorems

Abstract

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained include situations where the behavior is far from hyperbolic. We also give several new examples and show that our result includes as particular cases several previous theorems.