Liouvillian integration and Bernoulli foliations
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- by D. Cerveau and P. Sad PDF
- Trans. Amer. Math. Soc. 350 (1998), 3065-3081 Request permission
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.References
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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
- Received by editor(s): December 7, 1994
- Received by editor(s) in revised form: November 28, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 3065-3081
- MSC (1991): Primary 32L30; Secondary 58F18
- DOI: https://doi.org/10.1090/S0002-9947-98-01780-2
- MathSciNet review: 1390971