The existence of invariant curves of a kind of almost periodic twist mappings

TL;DR

This paper proves the existence of invariant curves in almost periodic twist mappings and applies these results to demonstrate the existence of almost periodic solutions and boundedness in pendulum equations with external forces.

Contribution

It establishes the existence of invariant curves in a new class of almost periodic twist mappings, extending the understanding of their dynamical behavior.

Findings

Existence of invariant curves in almost periodic twist mappings

Existence of almost periodic solutions for pendulum equations

Boundedness of all solutions in the studied system

Abstract

In this paper, we are concerned with the existence of invariant curves of the planar twist mappings where the perturbations are almost periodic. As an application, the existence of almost periodic solutions and the boundedness of all solutions for pendulum-type equations with an almost periodic external force are proved.