THE THEORY OF LEGENDRIAN UNFOLDINGS AND 1ST-ORDER DIFFERENTIAL-EQUATIONS

Authors
IZUMIYA S
Citation
S. Izumiya, THE THEORY OF LEGENDRIAN UNFOLDINGS AND 1ST-ORDER DIFFERENTIAL-EQUATIONS, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 123, 1993, pp. 517-532
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics → ACNP
ISSN journal
03082105
Volume
123
Year of publication
1993
Part
3
Pages
517 - 532
Database
ISI
SICI code
0308-2105(1993)123:<517:TTOLUA>2.0.ZU;2-D
Abstract
We consider some properties of completely integrable first-order diffe rential equations for real-valued functions. In order to study this su bject, we introduce the theory of Legendrian unfoldings. We give a cha racterisation of equations with classical complete solutions in terms of Legendrian unfoldings, and also assert that the set of equations wi th singular solutions is an open set in the space of completely integr able equations even though such a set is thin in the space of all equa tions.