Integration of complex differential equations
type: Item
instance of: scholarly article
title: Integration of complex differential equations
zbMATH Open document ID: 0958.34077
DOI: 10.1023/A:1021740700501
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: 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 \(p(x)dy -(y^2 a(x) +yb(x))dx=0.\)
Mathematics Subject Classification ID: 34M45
Mathematics Subject Classification ID: 37F75
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 1431875
zbMATH Keywords: holomorphic foliation
zbMATH Keywords: holonomy
zbMATH Keywords: Liouvillian function
zbMATH Keywords: affine transverse structure
author: Bruno Scárdua
MaRDI profile type: Publication
full work available at URL: a:1021740700501
OpenAlex ID: W2134699557
description: scientific article; zbMATH DE number 1431875