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ON THE NUMBER OF LIMIT CYCLES IN PERTURBATIONS OF A QUADRATIC REVERSIBLE CENTER

Part of: Qualitative theory Local and nonlocal bifurcation theory

Published online by Cambridge University Press:  11 October 2012

JUANJUAN WU ,
LINPING PENG  and
CUIPING LI
JUANJUAN WU*
Affiliation:
School of Math and System Sciences, Beihang University, Beijing, 100191, PR China (email: [email protected])
LINPING PENG
Affiliation:
School of Math and System Sciences, Beihang University, Beijing, 100191, PR China (email: [email protected])
CUIPING LI
Affiliation:
School of Math and System Sciences, Beihang University, Beijing, 100191, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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This paper is concerned with the bifurcation of limit cycles from a quadratic reversible system under polynomial perturbations. It is proved that the cyclicity of the period annulus is two, and also a linear estimate of the number of zeros of the Abelian integral for the system under polynomial perturbations of arbitrary degree nis given.

Keywords

Abelian integrallimit cyclescyclicityquadratic reversible system

MSC classification

Secondary: 34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) 37G15: Bifurcations of limit cycles and periodic orbits
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 3 , June 2012 , pp. 409 - 423
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc.

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