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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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