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Limit Cycles Close to Infinity of Certain Non-Linear Differential Equations

Published online by Cambridge University Press:  20 November 2018

Víctor Guíñez
Affiliation:
Universidad Técnica Federico Santa Maria, Departamento de Matemâtica, Casilla 110-V Valparaiso, Chile
Eduardo Sáez
Affiliation:
Universidad de Chile, Facultad de Ciencias, Las Paimeras 3425 Ñuñoa, Santiago, Chile
Iván Szántó
Affiliation:
Universidad de Chile, Facultad de Ciencias, Las Paimeras 3425 Ñuñoa, Santiago, Chile
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Abstract

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Through successive radial perturbations of a certain planar Hamiltonian polynomial vector field of degree 2K + 1, we obtain a least K limit cycles containing (2K + 1)2 singularities.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Coll, B., Gasull, A., and Llibre, J., Some theorems on the existence, uniqueness and non existence of limit cycles for Quadratic Systems, Journal of Differential Equations vol 67, No 3, (May 1987), 373399.Google Scholar
2. Coppel, W. A., A Survey of Quadratic Systems, Journal of Differential Equations vol 2 (1966), 293304.Google Scholar
3. Sotomayor, J. and Paterlini, R., Bifurcations of Polynomial vector fields in the plane. Oscillation, Bifurcation and chaos, American Math. Society, Providence (1987), 665-685, Atkinson, F. V., W. F. Langford and A. B. Mingarelli: Eds.Google Scholar
4. Jinghuang, Tian, On general properties of cubic systems, Int. J. Math. Educ, Sci. Technol. vol 14, No 5 (1983), 643648.Google Scholar
5. Andronov, A. A. et al., “Qualitative theory of Second Order Dynamic Systems,” Wiley, New York, 1973.Google Scholar