Integrability conditions for complex kukles systems

In this paper, we provide necessary and sufficient conditions for the existence of local analytic first integrals for a seventh-parameter family of complex cubic systems called the complex Kukles systems. The first author is partially supported by a MINECO/ FEDER [grant number MTM2014-53703-P]; an AGAUR (Generalitat de Catalunya) [grant number 2014SGR 1204]. The second author is supported by Portuguese National Funds through FCT - Fundação para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD.