Invariant Curves of Almost Periodic Reversible Mappings

TL;DR

This paper establishes invariant curve theorems for almost periodic reversible mappings and applies these results to demonstrate the existence of almost periodic solutions and boundedness in a nonlinear oscillator model.

Contribution

It introduces new invariant curve theorems for almost periodic reversible mappings and applies them to nonlinear oscillators with almost periodic forcing.

Findings

Existence of almost periodic solutions in nonlinear oscillators.

Boundedness of all solutions under certain conditions.

Invariant curve theorems for almost periodic reversible mappings.

Abstract

In this paper, we prove some invariant curve theorems for the planar almost periodic reversible mappings. As an application, we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the nonlinear oscillator $x"+g(x)x'+\varpi^{2}x+\varphi(x)=f(t)$ with $f(t)$ almost periodic.