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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 | Source: | 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. | Document URI: | http://hdl.handle.net/1942/2452 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/S0022-0396(02)00110-9 | ISI #: | 000180988300006 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2004 |
Appears in Collections: | Research publications |
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