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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Liouvillian integration and Bernoulli foliations


Authors: D. Cerveau and P. Sad
Journal: Trans. Amer. Math. Soc. 350 (1998), 3065-3081
MSC (1991): Primary 32L30; Secondary 58F18
MathSciNet review: 1390971
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Abstract: Analytic foliations in the 2-dimensional complex projective space with algebraic invariant curves are studied when the holonomy groups of these curves are solvable. It is shown that such a condition leads to the existence of a Liouville type first integral, and, under ``generic'' extra conditions, it is proven that these foliations can be defined by Bernoulli equations.


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Additional Information

D. Cerveau
Affiliation: Université de Rennes I - IRMAR, Campus de Beaulieu - 35042, Rennes, France

P. Sad
Affiliation: Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, CEP 22460-320 Rio de Janeiro, Brazil

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01780-2
PII: S 0002-9947(98)01780-2
Received by editor(s): December 7, 1994
Received by editor(s) in revised form: November 28, 1995
Article copyright: © Copyright 1997 American Mathematical Society