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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3256

Title: Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops
Authors: DUMORTIER, Freddy
Li, CZ
ZHANG, Zefan
Issue Date: 1997
Publisher: Academic Press
Citation: JOURNAL OF DIFFERENTIAL EQUATIONS, 139(1). p. 146-193
Abstract: In this paper we present a complete study of quadratic 3-parameter unfoldings of some integrable system belonging to the class Q(3)(R), and having two centers and two unbounded heteroclinic loops. We restrict to unfoldings that are transverse to Q(3)(R), obtain a versal bifurcation diagram and all global phase portraits, including the precise number and configuration of the limit cycles. It is proved that 3 is the maximal number of limit cycles surrounding a single focus, and only the (1, 1)-configuration can occur in case of simultaneous nests of limit cycles. Essentially the proof relies on a careful analysis of a related non-conservative Abelian integral. (C) 1997 Academic Press.
Notes: BEIJING UNIV,DEPT MATH,BEIJING 100871,PEOPLES R CHINA. BEIJING UNIV,MATH INST,BEIJING 100871,PEOPLES R CHINA.Dumortier, F, LIMBURGS UNIV CTR,UNIV CAMPUS,B-3590 DIEPENBEEK,BELGIUM.
URI: http://hdl.handle.net/1942/3256
DOI: 10.1006/jdeq.1997.3285
ISI #: A1997XU83200007
ISSN: 0022-0396
Type: Journal Contribution
Appears in Collections: Dynamical Systems

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