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Studies in multiplicative solutions to linear differential equations

Published online by Cambridge University Press:  14 November 2011

F. M. Arscott
F. M. Arscott
Affiliation:
Department of Applied Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
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Synopsis

Given an ordinary linear differential equation whose singularities are isolated, a solution is called multiplicative for a closed path C if, when continued analytically along C, it returns to its starting-point merely multiplied by a constant. This paper first classifies such paths into three types, then investigates combinations of two such paths, in which a number of qualitatively different situations can arise. A key result is also given relating to a three-path combination. There are applications to special functions and Floquet theory for periodic equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 277 - 305
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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