Symplectic structures underlie the equations of classical mechanics, and their properties are reflected in the behavior of a wide range of physical systems. Over the years much detailed information has accumulated about the behavior of particular systems. Powerful new methods, such as Gromov's flexibility theorem and proofs of the Arnold conjectures, have produced striking results, but the modern global theory of symplectic topology has only recently emerged. This book is an introduction to the subject for postgraduate students, presenting new methods in the field and providing proofs of the simpler versions of the most important new theorems. The deepest theorems in the book are proved by a new finite dimensional variational analysis which combines ideas from Viterbo's generating function approach with the infinite dimensional variational analysis of Hofer-Zehnder. Exercises are also included.
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Editorial Reviews
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On the first edition: "An authoritative and comprehensive reference...McDuff and Salamon have done an enormous service to the symplectic community: their book greatly enhances the accessibility of the subject to students and researchers alike." --Book Reviews, AMS
--This text refers to the Paperback edition.
About the Author
Dusa McDuff is one of the world's leading researchers in this field, and has been invited to speak at the International Congress of Mathematicians 1998.
--This text refers to the Paperback edition.
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12 of 14 people found the following review helpful:
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This review is from: Introduction to Symplectic Topology (Oxford Mathematical Monographs) (Paperback)
An authoritative and comprehensive reference...McDuff and Salamon have done an enormous service to the symplectic community: their book greatly enhances the accessibility of the subject to students and researchers alike.The discussion begins with classic topology and cover a variety of final year undergraduate topics such as complex manifolds and inverse differential techniques before moving into the vastly complex world of Symplectic Topology. A must for researchers new to the field
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First Sentence:
Symplectic structures first arose in the study of classical mechanical systems such as the planetary system, and almost all the classical work on symplectic geometry was focused on the attempt to understand how these systems behave. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonsqueezing theorem, nonsqueezing property, unitary trivialization, symplectic trivialization, flux homomorphism, symplectic action functional, symplectic fibration, exact symplectic manifold, symplectic isotopy, symplectic spectrum, linear symplectomorphism, symplectic ball, variational family, symplectic cylinder, symplectic rigidity, symplectic complement, plectic topology, symplectic vector bundles, symplectic embeddings, symplectic bundle, coisotropic submanifold, symplectomorphism groups, neighbourhood theorem, symplectic connection, symplectic vector fields Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Symplectic structures first arose in the study of classical mechanical systems such as the planetary system, and almost all the classical work on symplectic geometry was focused on the attempt to understand how these systems behave. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonsqueezing theorem, nonsqueezing property, unitary trivialization, symplectic trivialization, flux homomorphism, symplectic action functional, symplectic fibration, exact symplectic manifold, symplectic isotopy, symplectic spectrum, linear symplectomorphism, symplectic ball, variational family, symplectic cylinder, symplectic rigidity, symplectic complement, plectic topology, symplectic vector bundles, symplectic embeddings, symplectic bundle, coisotropic submanifold, symplectomorphism groups, neighbourhood theorem, symplectic connection, symplectic vector fields Key Phrases - Capitalized Phrases (CAPs): (learn more)
Use van Kampen New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 15
books:
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34
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- Differential Geometry (Proceedings of Symposia in Pure Mathematics, vol. 27, pt. 2) by Shiing-Shen Chern in Back Matter (1), and Back Matter (2)
- Partial Differential Equations (Lectures in Applied Mathematics) by L. Bers in Back Matter
- Floer Memorial Volume (Progress in Mathematics) by Helmut Hofer in Back Matter
- Torus Actions on Symplectic Manifolds (Progress in Mathematics) by Michèle Audin in Back Matter
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter
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- Symplectic Geometry and Topology (Ias/Park City Mathematics Series, V. 7) by Yakov Eliashberg on 4 pages
- Symmetry in Mechanics by Stephanie Frank Singer on page 143, and Back Matter
- Handbook of Differential Equations: Ordinary Differential Equations, Volume 2 by A. Canada on page 145
- An Introduction to Invariants and Moduli by Shigeru Mukai in Back Matter
- The Breadth of Symplectic and Poisson Geometry: Festschrift in Honor of Alan Weinstein (Progress in Mathematics) by Jerrold E. Marsden on page 170
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