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

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2019-01-14Suggested citation
García, I. A. (Isaac A.);
Maza Sabido, Susanna;
.
(2019)
.
Period annulus of the harmonic oscillator with zero cyclicity under perturbations with a homogeneous polynomial field.
Electronic Journal Of Qualitative Theory Of Differential Equations, 2019, vol. 3, p. 1-6.
https://doi.org/10.14232/ejqtde.2019.1.3.
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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.
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Electronic Journal Of Qualitative Theory Of Differential Equations, 2019, vol. 3, p. 1-6European research projects
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