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Linear meromorphic differential equations: A modern point of view


Author: V. S. Varadarajan
Journal: Bull. Amer. Math. Soc. 33 (1996), 1-42
MSC (1991): Primary 34A20, 13N05
DOI: https://doi.org/10.1090/S0273-0979-96-00624-6
MathSciNet review: 1339809
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Abstract: A large part of the modern theory of differential equations in the complex domain is concerned with regular singularities and holonomic systems. However the theory of differential equations with irregular singularities has a long history and has become very active in recent years. Substantial links of this theory to the theory of algebraic groups, commutative algebra, resurgent functions, and Galois differential methods have been discovered. This survey attempts a general introduction to some of these aspects, with emphasis on reduction theory, asymptotic analysis, Stokes phenomena, and certain moduli problems.


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Additional Information

V. S. Varadarajan
Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095-1555
Email: vsv@math.ucla.edu

Received by editor(s): October 24, 1994
Received by editor(s) in revised form: June 22, 1995
Additional Notes: This is a revised and expanded version of an invited hour talk at the AMS meeting in Portland, Oregon, June 15, 1991. Due to various personal circumstances its preparation has been delayed till now.
Article copyright: © Copyright 1996 American Mathematical Society