Overview

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.

Full Product Details

Author:   Alberto Abbondandolo ,  Alan Jeffrey (University of Newcastle upon Tyne, UK) ,  Haim Brezis ,  Ronald G. Douglas (Texas A & M University)
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
Volume:   425
Dimensions:   Width: 15.60cm , Height: 1.20cm , Length: 23.40cm
Weight:   0.280kg
ISBN:  

9781584882022

ISBN 10:   1584882026
Pages:   208
Publication Date:   15 March 2001
Audience:   Professional and scholarly ,  General/trade ,  Professional & Vocational ,  General
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Reviews

provides an interesting introduction to index theories in the study of periodic solutions of Hamiltonian systems the author presents some recently published results in the perspective of well-known ones and along the way he discusses several critical point techniques that could be useful in other problems. - Mathematical Reviews 2002

Author Information

Alberto Abbondandolo

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