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On the existence of algebraic differential equations with noded periodic solutions

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Radiophysics and Quantum Electronics Aims and scope

Abstract

It is proved that a system of three autonomous differential equations with polynomial (of the third degree and higher) right sides may have a noded closed curve as its solution.

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Literature cited

  1. R. Crowell and R. Fock, Introduction to the Theory of Nodes [Russian translation], Mir, Moscow (1967).

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  2. A. é. Reizin', Local Equivalence of Differential Equations [in Russian], Zinatne, Riga (1971).

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Authors and Affiliations

  1. Scientific-Research Institute of Applied Mathematics and Cybernetics, Gor'kii University, USSR

    Kh. Ganiev

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  1. Kh. Ganiev
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 3, pp. 389–392, March, 1972.

In conclusion the author deeply thanks Professor Yu. I. Neimark for his statement of the problem and the great interest that he manifested in its solution.

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Ganiev, K. On the existence of algebraic differential equations with noded periodic solutions. Radiophys Quantum Electron 15, 291–293 (1972). https://doi.org/10.1007/BF02210668

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  • DOI: https://doi.org/10.1007/BF02210668

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