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Transactions of the American Mathematical Society

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Sur les integrales premieres
dans la classe de Nilsson
d'equations differentielles holomorphes

Author: Frédéric Touzet
Journal: Trans. Amer. Math. Soc. 352 (2000), 1601-1622
MSC (1991): Primary 32-XX
Published electronically: December 7, 1999
MathSciNet review: 1675242
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Abstract: We study two classes of holomorphic differential equations. The first one is constitued by elements admitting solutions defined in an algebraic way (the so called Liouville class) and the second of elements admitting solutions defined in an analytic way (the Nilsson class). We build up links between these two classes using special properties of the holonomy and its results on the monodromy.

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Additional Information

Frédéric Touzet
Affiliation: Institut de Recherche Mathématique de Rennes, Université de Rennes, 35042 Rennes Cedex, France

Received by editor(s): June 11, 1997
Received by editor(s) in revised form: March 3, 1998
Published electronically: December 7, 1999
Article copyright: © Copyright 2000 American Mathematical Society