- Tytuł:
- Gradients and canonical transformations
- Autorzy:
- Zampieri, Gaetano
- Powiązania:
- https://bibliotekanauki.pl/articles/1293932.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
non-injective local diffeomorphisms
gradients
Legendre transform
canonical transformations - Opis:
- The main aim of this paper is to give some counterexamples to global invertibility of local diffeomorphisms which are interesting in mechanics. The first is a locally strictly convex function whose gradient is non-injective. The interest in this function is related to the Legendre transform. Then I show two non-injective canonical local diffeomorphisms which are rational: the first is very simple and related to the complex cube, the second is defined on the whole ℝ⁴ and is obtained from a recent important example by Pinchuk. Finally, a canonical transformation which is also a gradient (of a convex function) is provided.
- Źródło:
-
Annales Polonici Mathematici; 1999, 72, 2; 153-158
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł