In the first half of the paper, we consider singularities of infinitesimal contact transformations and first order partial differential equations, the main results being related to the classical Sternberg-Chen theorem for hyperbolic germs of vector fields. The second half explains how to construct global generating phase functions for solutions of Hamilton-Jacobi equations and see what their singularities look like.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-3,
author = {Marc Chaperon},
title = {Singularities in contact geometry},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {39-55},
zbl = {1064.37051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-3}
}
Marc Chaperon. Singularities in contact geometry. Banach Center Publications, Tome 60 (2003) pp. 39-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc62-0-3/