Rocky Mountain Journal of Mathematics

Liénard Limit Cycles Enclosing Period Annuli, or Enclosed by Period Annuli

M. Sabatini

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Rocky Mountain J. Math. Volume 35, Number 1 (2005), 253-266.

First available in Project Euclid: 5 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C05: Location of integral curves, singular points, limit cycles
Secondary: 58F14

Limit cycles polynomial systems Liénard systems 16th Hilbert's problem


Sabatini, M. Liénard Limit Cycles Enclosing Period Annuli, or Enclosed by Period Annuli. Rocky Mountain J. Math. 35 (2005), no. 1, 253--266. doi:10.1216/rmjm/1181069780.

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  • V.T. Borukhov, Qualitative behaviour of trajectories of a system of differential equations, Differential Equations 8 (1972), 1296-1297.
  • J. Chavarriga, H. Giacomini and J. Giné, On a new type of bifurcation of limit cycles for a planar cubic system, Nonlinear Anal. 36 (1999), 139-149.
  • C. Christopher, An algebraic approach to the classification of centers in polynomial Liénard systems, J. Math. Anal. Appl. 229 (1999), 319-329.
  • Dolov, Limit cycles in the case of a center, Differential Equations 8 (1972), 1304-1305.
  • F. Dumortier, R. E. Kooij and C. Li, Cubic Liénard equations with quadratic damping having two antisaddles, Qual. Theor. Dynam. Syst. 1 (2000), 163-211.
  • J.R. Graef, On the generalized Liénard equation with negative damping, J. Differential Equations 12 (1972), 34-62.
  • J. Hale, Ordinary differential equations, Pure Appl. Math., vol. 21 -1969.
  • R. Kooij and A. Zegeling, Coexistence of centers and limit cycles in polynomial systems, Rocky Mountain J. Math. 30 (2000), 621-640.
  • F. Marchetti, P. Negrini, L. Salvadori and M. Scalia, Liapunov direct method in approaching bifurcation problems, Ann. Mat. Pura Appl. (4) 108 (1976), 211-226.
  • M. Sabatini, Hopf bifurcation from infinity, Rend. Sem. Math. Univ. Padova 78 (1987), 237-253.
  • --------, Successive bifurcations at infinity for second order ODE's, Qual. Theor. Dynam. Syst. 3 (2002), 1-18.
  • D.S. Ushkho, On the coexistence of limit cycles and singular points of ``center'' type of cubic differential systems, Differential Equations 31 (1995), 163-164.
  • Ye Yan-Qian, et al., Theory of limit cycles, Transl. Math. Monographs, vol. 66, Amer. Math. Soc., Providence, Rhode Island, 1986.