Pfaffian Systems, k-Symplectic Systems

Awane, A.; Goze, M.

ISBN 10: 0792363736 / ISBN 13: 9780792363736

Published by Springer, 2000

A copy that has been read, remains in good condition. All pages are intact, and the cover is intact. The spine and cover show signs of wear. Pages can include notes and highlighting and show signs of wear, and the copy can include "From the library of" labels or previous owner inscriptions. 100% GUARANTEE! Shipped with delivery confirmation, if you're not satisfied with purchase please return item! Ships via media mail. Seller Inventory # OTV.0792363736.G

Synopsis:

The theory of foliations and contact forms have experienced such great de­ velopment recently that it is natural they have implications in the field of mechanics. They form part of the framework of what Jean Dieudonne calls "Elie Cartan's great theory ofthe Pfaffian systems", and which even nowa­ days is still far from being exhausted. The major reference work is. without any doubt that of Elie Cartan on Pfaffian systems with five variables. In it one discovers there the bases of an algebraic classification of these systems, their methods of reduction, and the highlighting ofthe first fundamental in­ variants. This work opens to us, even today, a colossal field of investigation and the mystery of a ternary form containing the differential invariants of the systems with five variables always deligthts anyone who wishes to find out about them. One of the goals of this memorandum is to present this work of Cartan - which was treated even more analytically by Goursat in its lectures on Pfaffian systems - in order to expound the classifications currently known. The theory offoliations and contact forms appear in the study ofcompletely integrable Pfaffian systems of rank one. In each of these situations there is a local model described either by Frobenius' theorem, or by Darboux' theorem. It is this type of theorem which it would be desirable to have for a non-integrable Pfaffian system which may also be of rank greater than one.

Synopsis: The geometrical view of mechanics is based on the study of certain exterior systems, the most classical of which are Pfaffian systems. In this book, we present the classification theorems (Frobenius, Darboux) and the local classification of Pfaffian systems of five variables, following Cartan. We also present a new class of exterior systems, called k-symplectic systems, generalizing the notion of symplectic form. These systems permit us to write in the language of exterior forms the equations proposed by Nambu for a model of statistical mechanics. This book is aimed at graduate students and at research workers in the field of mathematics, differential geometry, statistical mechanics, mathematics of physics and Lie algebras.

Bibliographic Details

Title: Pfaffian Systems, k-Symplectic Systems
Publisher: Springer
Publication Date: 2000
Binding: Hardcover
Condition: good