Bounded solutions of the finite and infinite-dimensional dynamical systems

TL;DR

This paper constructs invariant tori for finite and infinite-dimensional dynamical systems assuming exponential dichotomy, extending classical results and connecting with Palmer's lemma and prior work.

Contribution

It introduces new conditions for the existence of invariant tori in both finite and infinite-dimensional systems based on exponential dichotomy assumptions.

Findings

Invariant tori are constructed under exponential dichotomy conditions.

The main results relate closely to Palmer's lemma.

The work extends classical dynamical systems theory.

Abstract

Invariant torus are constructed under assumption that the homogeneous system admits an exponential dichotomy on the semi-axes. The main result is closely related with the well-known Palmer's lemma and results of Boichuk A.A., Samoilenko A.M.