Symplectic Invariants and Hamiltonian Dynamics

Eduard Zehnder

ISBN 10: 3034801033 / ISBN 13: 9783034801034

Published by Springer Basel Apr 2011, 2011

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 356 pp. Englisch.

Seller Inventory # 9783034801034

Bibliographic Details

• Title: Symplectic Invariants and Hamiltonian Dynamics
• Publisher: Springer Basel Apr 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 3034801033
• ISBN 13: 9783034801034
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.

About the Author

Helmut Hofer is Professor at the Institute for Advanced Study in Princeton, New Jersey, USA.

Eduard Zehnder is emeritus Professor of ETH Zürich, Switzerland.