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ON SECOND ORDER BIFURCATIONS OF LIMIT CYCLES

Published online by Cambridge University Press:  01 October 1998

I. D. ILIEV
I. D. ILIEV
Affiliation:
Institute of Mathematics, Bulgarian Academy of Sciences, PO Box 373, 1090 Sofia, Bulgaria. E-mail: [email protected]
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Abstract

The paper derives a formula for the second variation of the displacement function for polynomial perturbations of Hamiltonian systems with elliptic or hyperelliptic Hamiltonians H(x, y)=½y2−U(x) in terms of the coefficients of the perturbation. As an application, the conjecture stated by C. Chicone that a specific cubic system appearing in a deformation of singularity with two zero eigenvalues has at most two limit cycles is proved.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 353 - 366
Copyright
The London Mathematical Society 1998

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