Quasi-periodic motions in strongly dissipative forced systems

TL;DR

This paper investigates conditions under which strongly damped, quasi-periodically forced one-dimensional systems admit solutions with the same frequency as the forcing, contributing to understanding of dissipative dynamical systems.

Contribution

It establishes criteria for the existence of quasi-periodic solutions in strongly dissipative forced systems, extending previous results to a broader class of equations.

Findings

Conditions for existence of quasi-periodic solutions identified

Frequency matching between solutions and forcing established

Analysis applicable to a range of dissipative mechanical systems

Abstract

We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the forcing term for the existence of quasi-periodic solutions which have the same frequency vector as the forcing.