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  On Plane Polynomial Vector Fields and the Poincaré Problem

El Kahoui, M. (2002). On Plane Polynomial Vector Fields and the Poincaré Problem. Electronic journal of differential equations, 2002(37), 1-23.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0019-EBD5-C Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0023-F3DB-E
Genre: Journal Article
Latex : On Plane Polynomial Vector Fields and the {Poincar\'e} Problem

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El Kahoui, M'hammed1, Author           
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: In this paper we address the Poincaré problem, on plane polynomial vector fields, under some conditions on the nature of the singularities of invariant curves. Our main idea consists in transforming a given vector field of degree m into another one of degree at most m+1 having its invariant curves in projective quasi-generic position. This allows us to give bounds on degree for some well known classes of curves such as the nonsingular ones and curves with ordinary nodes. We also give a bound on degree for any invariant curve in terms of the maximum Tjurina number of its singularities and the degree of the vector field.

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Language(s): eng - English
 Dates: 2002
 Publication Status: Published online
 Pages: -
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 Identifiers: BibTex Citekey: ElKahoui2002b
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Title: Electronic journal of differential equations
Source Genre: Journal
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Publ. Info: San Marcos, Tex. : Published jointly by Southwest Texas State University and the University of North Texas
Pages: - Volume / Issue: 2002 (37) Sequence Number: - Start / End Page: 1 - 23 Identifier: ISSN: 1072-6691
CoNE: https://pure.mpg.de/cone/journals/resource/954926402639