A method for characterizing nilpotent centers
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To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the bifurcation of limit cycles from it or from its period annulus. We give an effective algorithm in the search of necessary conditions for detecting nilpotent centers based in recent developments. Moreover we survey the last results on this problem and illustrate our approach by means of examples.
Is part ofJournal of Mathematical Analysis and Applications, 2014, vol. 413, p. 537-545
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The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems Giacomini, Héctor; Giné, Jaume; Llibre, Jaume (Elsevier, 2006)In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov ...
García, I. A. (Isaac A.); Giacomini, Héctor; Giné, Jaume; Llibre, Jaume (Elsevier, 2016-04-25)We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré--Liapunov method to detect centers with purely imaginary ...
Grau Montaña, Maite; Llibre, Jaume (Elsevier, 2015)We consider a planar autonomous real analytic differential system with a monodromic singular point p. We deal with the center problem for the singular point p. Our aim is to highlight some relations between the divergence ...