Journal ArticleDOI
The Poincaré problem in the nondicritical case
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This article is published in Annals of Mathematics.The article was published on 1994-09-01. It has received 139 citations till now.read more
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MonographDOI
Lectures on analytic differential equations
TL;DR: Normal forms and desingularization Singular points of planar analytic vector fields Local and global theory of linear systems Functional moduli of analytic classification of resonant germs and their applications Global properties of complex polynomial foliations Appendix as mentioned in this paper.
Book ChapterDOI
Chapter 5 Integrability of polynomial differential systems
TL;DR: In this paper, the planar polynomial differential systems were introduced and the notion of first integral integral was introduced; and the definition of integrating factor was discussed. And the concept of an exponential factor due to Christopher was introduced.
Journal ArticleDOI
Some examples for the Poincaré and Painlevé problems
TL;DR: In this paper, the authors give examples of one-parameter families which show that both problems have a negative answer, and with some of the families they can also answer a question posed by M. Brunella in [5].
Journal ArticleDOI
Algebraic aspects of integrability for polynomial systems
Jaume Llibre,Colin Christopher +1 more
TL;DR: In this article, an introductory survey to the Darboux integrability theory of planar complex and real polynomial differential systems is presented, which contains some improvements to the classical theory.
Journal ArticleDOI
On some open problems in planar differential systems and Hilbert’s 16th problem
TL;DR: In this article, a brief summary of topics and concepts related with some open problems of planar differential systems is presented, most of them are related with 16th Hilbert problem which refers to the existence of a uniform upper bound on the number of limit cycles of a polynomial system in function of its degree.
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Journal ArticleDOI
Reduction of Singularities of the Differential Equation Ady = Bdx
TL;DR: In this paper, it was shown that the set S of solutions can be divided into a finite number of subsets Si, S = U Si, such that any pair in a given Si are equisingular in the sense of [1].
Journal ArticleDOI
Holonomie et intégrales premières
J.-F. Mattei,R. Moussu +1 more
TL;DR: Gauthier-Villars as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Journal ArticleDOI
Sur ĽintÉgration algÉbrique des Équations diffÉrentielles du premier ordre et du premier degrÉ
Journal ArticleDOI
Topological invariants and equidesingularization for holomorphic vector fields
TL;DR: The authors demontre un theoreme d'equidesingularisation, etudie l'invariance du nombre de Milnor et ses applications.