CATALOGO DEI PRODOTTI DELLA RICERCA
IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili.
EnglishThe 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 being related to the complex cube, the second is defined on the whole $R^4$ 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.
| Titolo: | Gradients and canonical transformations |
| Autori: | |
| Data di pubblicazione: | 1999 |
| Rivista: | |
| Abstract: | 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 being related to the complex cube, the second is defined on the whole $R^4$ 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. |
| Handle: | http://hdl.handle.net/11562/236600 |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
File in questo prodotto:
Copyright © 2020