The Legendre transformations on differential spaces (in the sense of Sikorski) is studied, and some properties for spaces with singularities are investigated. A mechanical interpretation of the Legendre transformation is also given.
@article{702133,
title = {The Legendre transformation in differential spaces},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1993},
pages = {[35]-46},
mrnumber = {MR1246618},
zbl = {0793.58005},
url = {http://dml.mathdoc.fr/item/702133}
}
Sasin, Wiesław; Multarzyński, Piotr. The Legendre transformation in differential spaces, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1993), pp. [35]-46. http://gdmltest.u-ga.fr/item/702133/