Geodesic
Complex periodic solutions of autonomous ODE systems with analytical right sides near an equilibrium point
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 393-398.

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The paper contains the proof of a theorem on the relation of frequencies of the periodic complex solutions of a nonlinear ordinary differential equation system resolved with respect to derivatives and having analytical right parts with the frequencies of periodic solutions of the corresponding linearized system in the neighborhood of an equilibrium point. 
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V. F. Edneral. Complex periodic solutions of autonomous ODE systems with analytical right sides near an equilibrium point. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 393-398. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a3/

[1] A. D. Bruno (Brjuno), “Analytical form of differential equations. I”, Trans. Mosc. Math. Soc., 25 (1971), 131–288 | MR

[2] A. D. Bruno (Brjuno), “Analytical form of differential equations. II”, Trans. Mosc. Math. Soc., 26 (1972), 199–239 | Zbl

[3] A. D. Bruno, Local Method in Nonlinear Differential Equations, Part I: The Local Method of Nonlinear Analyses of Differential Equations, Part II: The Sets of Analyticity of a Normalizing Transformation, Springer Series in Soviet Mathematics, 1988, 370 pp., ISBN 3-540-18926-2 | MR