Advances in Differential Equations

Higher-order Melnikov functions for degenerate cubic Hamiltonians

I. D. Iliev

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Abstract

It is shown that, in general, the first four Melnikov functions have to be taken into account in order to obtain definitive results concerning the limit cycles in quadratic perturbations of Hamiltonian systems in the plane with degenerate cubic Hamiltonians. An application is done in completing the proof that no more than two limit cycles can bifurcate out of homoclinic loops of quadratic Hamiltonian systems.

Article information

Source
Adv. Differential Equations Volume 1, Number 4 (1996), 689-708.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896033

Mathematical Reviews number (MathSciNet)
MR1401409

Zentralblatt MATH identifier
0851.34042

Subjects
Primary: 34C05: Location of integral curves, singular points, limit cycles
Secondary: 34C23: Bifurcation [See also 37Gxx] 34C37: Homoclinic and heteroclinic solutions 58F21

Citation

Iliev, I. D. Higher-order Melnikov functions for degenerate cubic Hamiltonians. Adv. Differential Equations 1 (1996), no. 4, 689--708. https://projecteuclid.org/euclid.ade/1366896033.


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