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Limit cycles bifurcanting from the period annulus of a uniform isochronous center in a quartic polynomial differential system
Itikawa, Jackson
Llibre, Jaume

Data: 2015
Resum: We study the number of limit cycles that bifurcate from the periodic solutions surrounding a uniform isochronous center located at the origin of the quartic polynomial differential system =-y xy(x^2 y^2), =x y^2(x^2 y^2), when it is perturbed inside the class of all quartic polynomial differential systems. Using the averaging theory of first order we show that at least 8 limit cycles can bifurcate from the period annulus of the considered center. Recently this problem was studied in Electron. J. Differ. Equ. 95 (2014), 1--14 where the authors only found 3 limit cycles.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Averaging theory ; Limit cycles ; periodic orbit ; Polynomial vector field ; uniform isochronous center
Publicat a: Electronic Journal of Differential Equations, Vol. 2015 Núm. 246 (2015) , p. 11 pages

13 p, 609.8 KB

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