Geodesic
The nonalgebraic character of the manifold of differential equations with rational right-hand sides and with multiple limit cycles
Sbornik. Mathematics, Tome 12 (1970) no. 3, pp. 453-457 
Yu. S. Ilyashenko. The nonalgebraic character of the manifold of differential equations with rational right-hand sides and with multiple limit cycles. Sbornik. Mathematics, Tome 12 (1970) no. 3, pp. 453-457. http://geodesic.mathdoc.fr/item/SM_1970_12_3_a6/
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     title = {The nonalgebraic character of the manifold of differential equations with rational right-hand sides and with multiple limit cycles},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathrm A^R_n$ denote the coefficient space of the equations $\frac{dy}{dx}=\frac{P_n(x,y)}{Q_n(x,y)}$, $(x,y)\in R^2$, where $P_n$ and $Q_n$ are polynomials of degree $n\geqslant2$, and let $M_k$ denote the set of equations $\alpha\in\mathrm A^R_n$ that have limit cycles of multiplicity not less than $k$. For $2\leqslant k\leqslant\frac{n(n+1)}2$ the set $M_k$ is not empty. A proof is given for the Theorem. The set $M_k$ does not form a semialgebraic manifold. Bibliography: 4 titles.

[4] V. I. Arnold, “Algebraicheskaya nerazreshimost problemy ustoichivosti po Lyapunovu i problemy topologicheskoi klassifikatsii osobykh tochek analiticheskoi sistemy differentsialnykh uravnenii”, Funk. analiz, 4:3 (1970), 1–9 | MR

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

[6] Yu. S. Ilyashenko, “Primer uravnenii $\dfrac{dw}{dz}=\dfrac{P_n(z,w)}{Q_n(z,w)}$, imeyuschikh schetnoe chislo predelnykh tsiklov i skol ugodno bolshoi zhanr po Petrovskomu–Landisu”, Matem. sb., 80(122) (1969), 388–404

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