Geodesic
Singular Points and First Integrals of Holomorphic Dynamical Systems
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 28-44

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We study the complex system $\dot z=F(z)$ near the singular point which is a multiple zero or a pole of the function $F(z)$ on the phase plane. We consider trajectories of such systems at infinity. We construct first integrals of polynomial systems using the method of Darboux. We use our results to sketch phase portraits.
Keywords: nonhyperbolic singular points, separatrices, elliptic sectors, hyperbolic sectors, first integrals. 
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     author = {E. P. Volokitin and V. M. Cheresiz},
     title = {Singular {Points} and {First} {Integrals} of {Holomorphic} {Dynamical} {Systems}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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     year = {2013},
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E. P. Volokitin; V. M. Cheresiz. Singular Points and First Integrals of Holomorphic Dynamical Systems. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 28-44. http://geodesic.mathdoc.fr/item/VNGU_2013_13_2_a3/