Period annulus of the harmonic oscillator with zero cyclicity under perturbations with a homogeneous polynomial field

Abstract

In this work we prove, using averaging theory at any order in the small perturbation parameter, that the period annulus of the harmonic oscillator has cyclicity zero (no limit cycles bifurcate) when it is perturbed by any fixed homogeneous polynomial field.

Keywords

• averaging theory
• periodic orbits
• poincaré map