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 ...
Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (American Institute of Mathematical Sciences, 2013-10)In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous ...
Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (Universitat Autònoma de Barcelona, 2014)In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic ...