## Rocky Mountain Journal of Mathematics

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

M. Sabatini

#### Article information

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

Dates
First available in Project Euclid: 5 June 2007

http://projecteuclid.org/euclid.rmjm/1181069780

Digital Object Identifier
doi:10.1216/rmjm/1181069780

Mathematical Reviews number (MathSciNet)
MR2117607

Zentralblatt MATH identifier
39.0563.02

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

#### Citation

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. http://projecteuclid.org/euclid.rmjm/1181069780.

#### References

• 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.