Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9083
Title: Limit cycles near hyperbolas in quadratic systems
Authors: Artes, Joan C.
DUMORTIER, Freddy 
Llibre, Jaurne
Issue Date: 2009
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 246(1). p. 235-260
Abstract: In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics Dl(2a) from the programme, set up in [F. Dumorlier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability. (c) 2008 Elsevier Inc. All rights reserved.
Notes: [Dumortier, Freddy] Univ Hasselt, Dept Math, B-3590 Diepenbeek, Belgium. [Artes, Joan C.; Llibre, Jaurne] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain.
Keywords: Limit cycle; Quadratic vector field; Strip of hyperbolas
Document URI: http://hdl.handle.net/1942/9083
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2008.06.032
ISI #: 000261314600011
Category: A1
Type: Journal Contribution
Validations: ecoom 2009
Appears in Collections:Research publications

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