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|Title: ||Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops|
|Authors: ||DUMORTIER, Freddy|
|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.|
|ISI #: ||A1997XU83200007|
|Type: ||Journal Contribution|
|Appears in Collections: ||Dynamical Systems|
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