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The theory of Legendrian unfoldings and first-order differential equations

Published online by Cambridge University Press:  14 November 2011

Shyuichi Izumiya
Shyuichi Izumiya
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060, Japan
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Synopsis

We consider some properties of completely integrable first-order differential equations for real-valued functions. In order to study this subject, we introduce the theory of Legendrian unfoldings. We give a characterisation of equations with classical complete solutions in terms of Legendrian unfoldings, and also assert that the set of equations with singular solutions is an open set in the space of completely integrable equations even though such a set is thin in the space of all equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 3 , 1993 , pp. 517 - 532
Copyright
Copyright © Royal Society of Edinburgh 1993

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