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On the existence of algebraic differential equations with noded periodic solutions

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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. 1.

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

  2. 2.

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

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Additional information

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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Keywords

  • Differential Equation
  • Periodic Solution
  • Quantum Electronics
  • Nonlinear Optic
  • Closed Curve