Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems
type: Item
instance of: scholarly article
title: Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems
zbMATH Open document ID: 0661.58013
DOI: 10.1016/0022-0396(88)90065-4
author: Richard C. Churchill
author: David L. Rod
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: The classical approach, namely the series representation of solutions, is applied to obtain the generators for the monodromy group of complex Hamiltonian systems. Two other ways are discussed as well. The complex linear differential equations are regarded as holomorphic connections on holomorphic vector bundles over Riemann surfaces. The special attention is paid, with respect to \textit{S. L. Ziglin}'s Non-integrability Theorem [Funct. Anal. Appl. 16, 181-189 (1983); translation from Funkts. Anal. Prilozh. 16, No.3, 30-41 (1982; Zbl 0524.58015)], to the computation of a monodromy group to the hypergeometric equation.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 4080443
zbMATH Keywords: non-integrability
zbMATH Keywords: monodromy group
zbMATH Keywords: complex Hamiltonian systems
reviewed by: Jan Andres
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90065-4
OpenAlex ID: W1965136018
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description: scientific article; zbMATH DE number 4080443