Symplectic invariants and Hamiltonian dynamics
著者
書誌事項
Symplectic invariants and Hamiltonian dynamics
（Modern Birkhäuser classics）
Birkhäuser, 2011
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注記
"Originally published under the same title in the Birkhäuser advanced texts : Basler Lehrbücher series by Birkhäuser Verlag, Switzerland, ISBN 978-3-7643-5066-6. Reprinted 2011 by Springer Basel AG"--T.p. verso
"Reprint of the 1994 edition"--T.p
Includes index
内容説明・目次
内容説明
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.
目次
1 Introduction.- 2 Symplectic capacities.- 3 Existence of a capacity.- 4 Existence of closed characteristics.- 5 Compactly supported symplectic mappings in R2n.- 6 The Arnold conjecture, Floer homology and symplectic homology.- Appendix.- Index.- Bibliography.
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