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The number of limit cycles for a class of quintic Hamiltonian systems under quintic perturbations

Part of: Qualitative theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  09 April 2009

Guowei Chen ,
Yongbin Wu  and
Xinan Yang
Xinan Yang
Affiliation:
Department of Mathematics, Fuzhou University, Fuzhou 350002, China e-mail: gnchen@fzu.edu.cn
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Abstract

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The Hopf bifurcation and homoclinic bifurcation of the quintic Hamiltonian system is analyzed under quintic perturbations by using unfolding theory in this paper. We show that a quintic system can have at least 29 limit cycles.

Keywords

quintic Hamiltonian systemlimit cyclebifurcation

MSC classification

Secondary: 34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) 37C10: Vector fields, flows, ordinary differential equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 37 - 54
Copyright
Copyright © Australian Mathematical Society 2002

References

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