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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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