Morse theory for Hamiltonian systems
著者
書誌事項
Morse theory for Hamiltonian systems
（Research notes in mathematics, 425）（A Chapman & Hall book）
CRC Press, 2018, c2001
- : hardback
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注記
Bibliography: p. 173-186
Includes index
内容説明・目次
内容説明
This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, until now, have appeared only in scattered journals.
Morse Theory for Hamiltonian Systems provides a detailed description of the Maslov index, introduces the notion of relative Morse index, and describes the functional setup for the variational theory of Hamiltonian systems, including a new proof of the equivalence between the Hamiltonian and the Lagrangian index. It also examines the superquadratic Hamiltonian, proving the existence of periodic orbits that do not necessarily satisfy the Rabinowitz condition, studies asymptotically linear systems in detail, and discusses the Arnold conjectures about the number of fixed points of Hamiltonian diffeomorphisms of compact symplectic manifolds.
In six succinct chapters, the author provides a self-contained treatment with full proofs. The purely abstract functional aspects have been clearly separated from the applications to Hamiltonian systems, so many of the results can be applied in and other areas of current research, such as wave equations, Chern-Simon functionals, and Lorentzian geometry. Morse Theory for Hamiltonian Systems not only offers clear, well-written prose and a unified account of results and techniques, but it also stimulates curiosity by leading readers into the fascinating world of symplectic topology.
目次
The Morse Index. The Relative Morse Index. Functional Setting. Superquadratic Hamiltonians. Asymptotically Linear Systems. The Arnold Conjectures for Symplectic Fixed Points. Index. References.
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