Integrability of complex planar systems with homogeneous nonlinearities
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In this paper we obtain sufficient conditions for the existence of a local analytic first integral for a family of quintic systems having homogeneous nonlinearities. The family studied in this work is the largest one classified until now for systems with such nonlinearities. We propose also an approach to find reversible systems within polynomial families of Lotka-Volterra systems with homogeneous nonlinearities.
Is part ofJournal of Mathematical Analysis and Applications, 2016, vol. 434, núm. 1, p. 894-914
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Giné, Jaume; Romanovski, Valery G. (Elsevier, 2010)In this paper we obtain necessary and sufficient integrability conditions at the origin for the Lotka–Volterra complex quintic systems which are linear systems perturbed by fifth degree homogeneous polynomials, i.e., we ...
Dukaric, Masa; Giné, Jaume; Llibre, Jaume (Elsevier, 2016)We provide 13 non--topological equivalent classes of global phase portraits in the Poincaré disk of reversible cubic homogeneous systems with a nilpotent center at origin, which complete the classification of the phase ...
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. ...