The number of limit cycles due to polynomial perturbations of the harmonic oscillator

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 127, Issue 2, 1999, Pages 317-322

  Iliev, Iliya D ^a  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844455226     PISSN: 03050041     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0305004199003795     Document Type: Article

References (7)

1. N. N. BAUTIN. On the number of limit cycles which appear with the variations of the coefficients from an equilibrium point of focus or center type. In: AMS Translations-Series 1, 5 (1962), 396-413
2. [Russian original: Mat. Sbornik 30 (1952), 181-196].
3. J.-P. FRANÇOISE. Successive derivatives of a first return map, application to the study of quadratic vector fields. Ergod. Theory Dynam. Syst. 16 (1996), no. 1, 87-96.
4. I. D. ILIEV. On second order bifurcations of limit cycles. J. Lond. Math. Soc. 58 (1998), 353-366.
5. L. M. PERKO. Differential equations and dynamical systems, 2nd edition. Texts in Applied Mathematics 7 (Springer, 1996).
6. R. ROUSSARIE. Bifurcations of planar vector fields and Hilbert's 16th problem (IMPA, 1995).
7. H. ŻOŁADEK. On a certain generalization of Bautin's theorem. Nonlinearity 7 (1994), 273-279.