# Resonance of bounded isochronous oscillators

## TL;DR

This paper investigates the conditions under which a bounded isochronous oscillator experiences resonance when subjected to periodic forcing, leading to solutions escaping the bounded region.

## Contribution

It provides a sufficient condition on the perturbation that guarantees resonance in bounded isochronous oscillators, a novel insight into their dynamic behavior.

## Key findings

- Resonance causes solutions to escape the period annulus.
- A specific sufficient condition on the perturbation is identified.
- The results apply to bounded isochronous oscillators with a common period.

## Abstract

An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the phenomenon of resonance may appear. We give a sufficient condition on the perturbation in order that resonance occurs when the period annulus of the isochronous oscillator is bounded. In this context, resonance means that all solutions escape from the period annulus.