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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.
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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.
Review
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)
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- PublisherBirkhäuser
- Publication date2011
- ISBN 10 3034801033
- ISBN 13 9783034801034
- BindingPaperback
- LanguageEnglish
- Number of pages355
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Softcover. Condition: Near Fine. Reprint. A bright, solid book, card covers are clean and crisp, text unmarked. ; Modern Birkhäuser Classics; 9.25 X 6.10 X 0.81 inches; 341 pages; "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.". Seller Inventory # 17875
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Symplectic Invariants and Hamiltonian Dynamics
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ISBN 10: 3034801033
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Taschenbuch. Condition: Neu. 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
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Symplectic Invariants and Hamiltonian Dynamics
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783034801034
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