Liouvillian integration and Bernoulli foliations

Cerveau, D.; Sad, P.

doi:10.1090/S0002-9947-98-01780-2

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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