Integrability conditions of a resonant saddle perturbed with homogeneous quintic nonlinearities
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In this work we complete the integrability conditions (i.e. conditions for the existence of a local analytic first integral) for a family of a resonant saddle perturbed with homogeneous quintic nonlinearities studied in a previous work. In order to obtain the necessary conditions we use modular arithmetic computations.
Is part ofNonlinear Dynamics, 2015, vol. 81, núm. 4, p. 2021-2030
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Giné, Jaume; Valls, Claudia (Elsevier, 2016)We consider a complex differential system with a resonant saddle that remind the classical Liénard systems in the real plane. For such systems we determine the conditions of analytic integrability of the resonant saddle.
Fercec, Brigita; Giné, Jaume; Romanovski, Valery G.; Edneral, Victor F. (Elsevier, 2016)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 ...
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 ...