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A class of planar quadratic vector fields with a limit cycle surrounded by a saddle loop


Author: Rodrigo Bamón
Journal: Proc. Amer. Math. Soc. 88 (1983), 719-724
MSC: Primary 58F21; Secondary 34C05
DOI: https://doi.org/10.1090/S0002-9939-1983-0702307-7
MathSciNet review: 702307
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Abstract: Examples of planar quadratic vector fields with a limit cycle surrounded by a saddle loop are given by means of deformations of Hamiltonian vector fields.


References [Enhancements On Off] (What's this?)

  • [CL] E. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 0069338 (16:1022b)
  • [ChSh] C. Chicone and D. Shafer, Separatrix and limit cycles of quadratic systems and Dulac's theorem, Trans. Amer. Math. Soc. (to appear). MR 701513 (84m:58110)
  • [ChT] C. Chicone and Tian Jinghiang, On general properties of quadratic systems, Amer. Math. Monthly 89 (1982), no. 3. MR 645790 (84f:34044)
  • [S] J. Sotomayor, Estabilidade estrutural de primeira ordem e variedades de Banach, Thesis, IMPA, Brazil, 1964.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0702307-7
Keywords: Limit cycle, quadratic systems, saddle loop, Hamiltonian
Article copyright: © Copyright 1983 American Mathematical Society

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