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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 | Source: | 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. | Document URI: | http://hdl.handle.net/1942/3256 | DOI: | 10.1006/jdeq.1997.3285 | ISI #: | A1997XU83200007 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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