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, 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 ...
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 i Embid, Armengol; Giné, Jaume (Springer International Publishing, 2017)We characterize the local analytic integrability of weak saddles for complex Lienard systems, x˙ = y−F(x), y˙ = ax, 0 = a ∈ C, with F analytic at 0 and F(0) = F (0) = 0. We prove that they are locally integrable at the ...