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/