Analytic Tools to Bound the Criticality at the Outer Boundary of the Period Annulus
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-016-9559-x
Abstract: In this paper we consider planar potential differential systems and we study the bifurcation of critical periodic orbits from the outer boundary of the period annulus of a center. In the literature the usual approach… read more here.
Keywords: period function; outer boundary; analytic tools; period ... See more keywords
Period annulus of the harmonic oscillator with zero cyclicity under perturbations with a homogeneous polynomial field
Sign Up to like & getrecommendations! Published in 2019 at "Electronic Journal of Qualitative Theory of Differential Equations"
DOI: 10.14232/ejqtde.2019.1.3
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… read more here.
Keywords: period annulus; homogeneous polynomial; harmonic oscillator; annulus harmonic ... See more keywords