LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	516.36
Title	Pfaffian Systems, k-Symplectic Systems ([EBook] /) / by Azzouz Awane, Michel Goze.
Author	Awane, Azzouz
Added Personal Name	Goze, Michel author.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands : : Imprint: Springer, , 2000.
Physical Details	XIII, 240 p. 1 illus. : online resource.
ISBN	9789401595261
Summary Note	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.:
Contents note	1 Exterior Forms -- 2 Exterior Systems -- 3 k-Symplectic Exterior Systems -- 4 Pfaffian Systems -- 5 Classification of Pfaffian Systems -- 6 k-Symplectic Manifolds -- 7 k-Symplectic Affine Manifolds -- 8 Homogeneous k-Symplectic G-Spaces -- 9 Geometric Pre-Quantization.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-015-9526-1
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Differential Geometry . Dynamical Systems . Engineering mathematics . Mathematics . Non-associative Rings and Algebras . Nonassociative rings . Rings (Algebra) . Statistical Physics . Statistical Physics, Dynamical Systems and Complexity . Authors: Awane, Azzouz . Goze, Michel . Corporate Authors: SpringerLink (Online service) . Classification: 516.36 .

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Pfaffian Systems, k-Symplectic Systems

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