Integration of complex differential equations
The problem of integration of complex differential equations is considered from several viewpoints: Liouvillian integration, the study of the holonomy groups associated with compact leaves of the holomorphic foliation subjacent to the differential equation and construction of the transverse structure of the foliation. Sufficient conditions are proved for the holomorphic foliation \(\mathcal F\) on \(CP(2)\) with generic singularities under which either \(\mathcal F\) is given by a closed rational (meromorphic) 1-form or it is a rational (meromorphic) pull-back from a Bernoulli foliation \(p(x)dy -(y^2 a(x) +yb(x))dx=0.\)
scientific article; zbMATH DE number 1431875