Geodesic
An example of eqations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ having a countable number of limit cycles and arbitrarily large Petrovskii–Landis genus
Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 365-378 
Yu. S. Ilyashenko. An example of eqations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ having a countable number of limit cycles and arbitrarily large Petrovskii–Landis genus. Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 365-378. http://geodesic.mathdoc.fr/item/SM_1969_9_3_a5/
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     title = {An example of eqations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ having a~countable number of limit cycles and arbitrarily large {Petrovskii{\textendash}Landis} genus},
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     pages = {365--378},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this work we construct an open set $V$ in the space of coefficients $A_n$ of the equations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ such that on the solutions of an arbitrary equation $\alpha\in V$ there exist a countable number of homotopically distinct limit cycles. Also, for each natural number $N$ we construct an open set $V_N\subset A_n$ such that an arbitrary equation $\alpha\in V_N$ has a Petrovskii–Landis genus which exceeds $N$. Bibliography: 9 titles.

[1] I. G. Petrovskii, E. M. Landis, “O chisle predelnykh tsiklov uravneniya $\dfrac{dy}{dx}=\dfrac{P(x,y)}{Q(x,y)}$, gde $P$ i $Q$ – mnogochleny vtoroi stepeni”, Matem. sb., 37(79):2 (1955), 209–250 | MR | Zbl

[2] Yu. S. Ilyashenko, “Vozniknovenie predelnykh tsiklov pri vozmuschenii uravneniya $\frac{dw}{dz}=-\frac{R_z}{R_w}$, gde $R(z,w)$ – mnogochlen”, Matem. sb., 78(120) (1969), 360–373

[3] B. A. Fuks, Vvedenie v teoriyu analiticheskikh funktsii mnogikh kompleksnykh peremennykh, Fizmatgiz, M., 1962 | MR

[4] A. B. Zhizhchenko, “O gruppakh gomologii algebraicheskikh mnogoobrazii”, Izv. AN SSSR, seriya matem., 25 (1961), 765–788 | Zbl

[5] Dzh. Springer, Vvedenie v teoriyu rimanovykh poverkhnostei, IL, M., 1960

[6] G. Stolzenberg, “Uniform approximation on smooth curves”, Acta Math., 115:3,4 (1966), 185–198 | DOI | MR | Zbl

[7] M. G. Khudai-Vepenov, “Ob odnom svoistve reshenii odnogo differentsialnogo uravneniya”, Matem. sb., 56(98) (1962), 301–308

[8] Yu. S. Ilyashenko, “Plotnost individualnogo resheniya i ergodichnost semeistva reshenii uravneniya $\frac{d\xi}{d\eta}=\frac{P(\xi,\eta)}{Q(\xi,\eta)}$”, Matem. zametki, 4 (1968), 741–750 | MR

[9] I. G. Petrovskii, E. M. Landis, “Popravki k statyam "O chisle predelnykh tsiklov uravneniya $\frac{dy}{dx}=\frac{P(x,y)}{Q(x,y)}$, gde $P$ i $Q$ – mnogochleny vtoroi stepeni" i "O chisle predelnykh tsiklov uravneniya $\frac{dy}{dx}=\frac{P(x,y)}{Q(x,y)}$, gde $P$ i $Q$ – polinomy"”, Matem. sb., 48(90) (1959), 253–255 | MR | Zbl