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Elliptic integrals and limit cycles

Published online by Cambridge University Press:  17 April 2009

A.M. Urbina ,
M. León De La Barra ,
G. León De La Barra  and
M. Cañas
A.M. Urbina
Affiliation:
Universidad Técnica, Federico Santa María Departamento de Matemática Casilla 110 – V Valparaíso, Chile
M. León De La Barra
Affiliation:
Universidad Técnica, Federico Santa María Departamento de Matemática Casilla 110 – V Valparaíso, Chile
G. León De La Barra
Affiliation:
Universidad Técnica, Federico Santa María Departamento de Matemática Casilla 110 – V Valparaíso, Chile
M. Cañas
Affiliation:
Universidad Técnica, Federico Santa María Departamento de Matemática Casilla 110 – V Valparaíso, Chile
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By using zeros of elliptic integrals we establish an upper bound for the number of limit cycles that emerge from the period annulus of the Hamiltonian XH in the system Xε = XH + ε(P, Q), where H = y2 + x4 and P, Q are polynomials in x, y, as a function of the degrees of P and Q. In particular, if (P, Q) = , with N = 2k + 1 or 2k + 2, this upper bound is k − 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 195 - 200
Copyright
Copyright © Australian Mathematical Society 1993

References

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