On the meromorphic equivalence of standard matrix differential equations

Article type: Research Article

Authors: Jurkat, W.B. | Zwiesler, H.J.

Affiliations: Abteilung Mathematik V, Universitaet Ulm, Oberer Eselsberg, D-7900 Ulm/Donau, Fed. Rep. Germany

Abstract: In this paper we address the problem of determining all the meromorphic differential equations that are meromorphically equivalent to a given equation; and we also discuss how one can effectively check whether two given equations are equivalent. In the case of equations of block size 1, which is a generalization of the case of distinct eigenvalues, we provide solutions to these problems which involve only algebraic processes. This allows a detailed description of the structure of the involved transformations. Our discussion is based on the concept of direct transformations which we define and study thoroughly.

DOI: 10.3233/ASY-1988-1403

Journal: Asymptotic Analysis, vol. 1, no. 4, pp. 303-316, 1988