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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2452

Title: Perturbation from an elliptic Hamiltonian of degree four - III global centre
Authors: DUMORTIER, Freddy
Li, CZ
Issue Date: 2003
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: JOURNAL OF DIFFERENTIAL EQUATIONS, 188(2). p. 473-511
Abstract: The paper deals with Lienard equations of the form <(x)over dot> = y, (y) over circle = P(x) + yQ(x) with P and Q polynomials of degree, respectively, 3 and 2. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree four, exhibiting a global centre. It is proven that the least upper bound of the number of zeros of the related elliptic integral is four, and this is a sharp one. This result permits to prove the existence of Lienard equations of type (3,2) with a quadruple limit cycle, with both a triple and a simple limit cycle, with two semistable limit cycles, with one semistable and two simple limit cycles or with four simple limit cycles. (C) 2002 Elsevier Science (USA). All rights reserved.
Notes: Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium. Peking Univ, Dept Math, Beijing 100871, Peoples R China.Dumortier, F, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/2452
DOI: 10.1016/S0022-0396(02)00110-9
ISI #: 000180988300006
ISSN: 0022-0396
Category: A1
Type: Journal Contribution
Validation: ecoom, 2004
Appears in Collections: Research publications

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