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• Integrability conditions of a resonant saddle in Liénard-like complex systems 

  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.

• Centers for the Kukles homogeneous systems with odd degree 

  Giné, Jaume; Llibre, Jaume; Valls, Claudia (London Mathematical Society, 2015)

  For the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for ...

• Integrability of complex planar systems with homogeneous nonlinearities 

  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 ...