Center cyclicity of a family of quartic polynomial differential system
MetadataShow full item record
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 nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.
Is part ofNonlinear Differential Equations and Applications-NoDEA, 2016, vol. 23, n. 34
Showing items related by title, author, creator and subject.
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2015-01-20)We consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the ...
García, I. A. (Isaac A.); Maza Sabido, Susanna; Shafer, Douglas S. (Elsevier, 2018-11-09)This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-known Lorenz family, and also in the Chen and Lü families. We prove that at most one limit cycle can be made to bifurcate from ...
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2013)First we provide new properties about the vanishing multiplicity of the inverse integrating factor of a planar analytic differential system at a focus. After we use this vanishing multiplicity for studying the cyclicity ...