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1996 Higher-order Melnikov functions for degenerate cubic Hamiltonians
I. D. Iliev
Adv. Differential Equations 1(4): 689-708 (1996).

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.

Citation

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I. D. Iliev. "Higher-order Melnikov functions for degenerate cubic Hamiltonians." Adv. Differential Equations 1 (4) 689 - 708, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0851.34042
MathSciNet: MR1401409

Subjects:
Primary: 34C05
Secondary: 34C23, 34C37, 58F21

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 4 • 1996
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