Study of the cyclicity of some degenerate graphics inside quadratic systems

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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