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This article is cited in 11 scientific papers (total in 11 papers)
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
Yu. S. Ilyashenko
Abstract:
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.
Received: 04.02.1969
Citation:
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”, Mat. Sb. (N.S.), 80(122):3(11) (1969), 388–404; Math. USSR-Sb., 9:3 (1969), 365–378
Linking options:
https://www.mathnet.ru/eng/sm3625https://doi.org/10.1070/SM1969v009n03ABEH001288 https://www.mathnet.ru/eng/sm/v122/i3/p388
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Abstract page: | 661 | Russian version PDF: | 143 | English version PDF: | 8 | References: | 58 | First page: | 3 |
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