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Author, Editor(s)

Author(s):

El Kahoui, M'hammed

dblp



BibTeX cite key*:

ElKahoui2002b

Title

Title*:

On plane polynomial vector fields and the Poincar\'e problem

Journal

Journal Title*:

Electronic Journal of Differential Equations

Journal's URL:

http://ejde.math.swt.edu/index.html

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Language:

English

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Name:


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Address:


ISSN:

1072-6691

Vol, No, pp, Date

Volume*:

2002

Number:

37

Publishing Date:

2002

Pages*:

1-23

Number of
VG Pages:

23

Page Start:

1

Page End:

23

Sequence Number:


DOI:


Note, Abstract, ©

Note:


(LaTeX) Abstract:

In this paper we address the Poincar\'e 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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Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

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BibTeX Entry:

@ARTICLE{ElKahoui2002b,
AUTHOR = {El Kahoui, M'hammed},
TITLE = {On plane polynomial vector fields and the {P}oincar\'e problem},
JOURNAL = {Electronic Journal of Differential Equations},
YEAR = {2002},
NUMBER = {37},
VOLUME = {2002},
PAGES = {1--23},
ISBN = {1072-6691},
}


Entry last modified by Christine Kiesel, 07/15/2014
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Editor(s)
[Library]
Created
02/25/2005 03:19:26 PM
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Editor
Christine Kiesel
M'hammed El Kahoui


Edit Date
22.04.2005 14:09:14
02/25/2005 03:19:26 PM