Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9651
Title: STUDY OF THE CYCLICITY OF SOME DEGENERATE GRAPHICS INSIDE QUADRATIC SYSTEMS
Authors: DUMORTIER, Freddy 
Rousseau, Christiane
Issue Date: 2009
Publisher: AMER INST MATHEMATICAL SCIENCES
Source: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 8(4). p. 1133-1157
Abstract: In this paper we make essential steps in proving the finite cyclicity of degenerate graphics in quadratic systems, having a line of singular points in the finite plane. In particular we consider the graphics (DF1a), (DF2a) of the program of [8] to prove the finiteness part of Hilbert's 16th problem for quadratic vector fields. We make a complete treatment except for one very specific problem that we clearly identify.
Notes: [Dumortier, Freddy] Hasselt Univ, Hasselt, Belgium. [Rousseau, Christiane] Univ Montreal, DMS, Montreal, PQ H3C 3J7, Canada. [Rousseau, Christiane] Univ Montreal, CRM, Montreal, PQ H3C 3J7, Canada.
Keywords: Finite cyclicity; singular perturbations; blow-up of the family; degenerate graphics; Hilbert's 16-th problem for quadratic systems
Document URI: http://hdl.handle.net/1942/9651
ISSN: 1534-0392
e-ISSN: 1553-5258
DOI: 10.3934/cpaa.2009.8.1133
ISI #: 000265190400001
Category: A1
Type: Journal Contribution
Validations: ecoom 2010
Appears in Collections:Research publications

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