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TitleDynamical Systems IV [electronic resource] : Symplectic Geometry and its Applications / edited by V. I. Arnol'd, S. P. Novikov
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1990
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Descript VII, 286 p. 2 illus. online resource


This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field


Contents: Linear Symplectic Geometry: Symplectic Manifolds -- Symplectic Geometry and Mechanics. Contact Geometry. Lagrangian and Legendre Singularities. Lagrangian and Legendre Cobordism -- References

Mathematics Topological groups Lie groups Mathematical analysis Analysis (Mathematics) Differential geometry Topology Physics Mathematics Analysis Theoretical Mathematical and Computational Physics Differential Geometry Topological Groups Lie Groups Topology


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