Cyclicity versus center problem
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We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.
Is part ofQualitative Theory of Dynamical Systems, 2010, vol. 9, núm. 1-2, p. 101-113
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Gasull i Embid, Armengol; Giné, Jaume; Torregrosa, Joan (American Institute of Mathematical Sciences, 2016)We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. ...
Gasull, Armengol; Giné, Jaume; Valls, Claudia (Elsevier, 2017)We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems ...
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Springer, 2016-09-01)In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any ...