Overview
- Opened new perspectives for the old field of Hamiltonian systems and let to the creation of a new field: symplectic topology
- Invariants which grew out of lectures given by the authors
- Selection by a single principle: the action principle of mechanics
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (6 chapters)
Keywords
About this book
The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology.
The exposition is self-contained and addressed to researchers and students from the graduate level onwards.
Reviews
From the reviews:
“Symplectic Invariants and Hamiltonian Dynamics is obviously a work of central importance in the field and is required reading for all would-be players in this game. Happily, it is very well written and sports a lot of very useful commentary by the authors; the sections introducing the individual chapters are particularly well done … . It is all fine scholarship in an exciting and fertile area.” (Michael Berg, The Mathematical Association of America, June, 2011)
Authors and Affiliations
About the authors
Helmut Hofer is Professor at the Institute for Advanced Study in Princeton, New Jersey, USA.
Eduard Zehnder is emeritus Professor of ETH Zürich, Switzerland.
Bibliographic Information
Book Title: Symplectic Invariants and Hamiltonian Dynamics
Authors: Helmut Hofer, Eduard Zehnder
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0348-0104-1
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel AG 2011
Softcover ISBN: 978-3-0348-0103-4Published: 02 April 2011
eBook ISBN: 978-3-0348-0104-1Published: 31 March 2011
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XIV, 341
Number of Illustrations: 49 b/w illustrations
Topics: Differential Geometry, Manifolds and Cell Complexes (incl. Diff.Topology), Analysis