Morse Theory for Hamiltonian Systems
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A01=Alberto Abbondandolo
asymptotically linear systems
Author_Alberto Abbondandolo
Category=PBKJ
Closed Subspaces
complement
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Finite Dimensional
Finite Dimensional Reductions
fixed points in symplectic manifolds
Floquet Multipliers
fredholm
Fredholm Index
Fredholm Operator
Hamiltonian System
Hamiltonian Vector Field
hilbert
Hilbert Manifold
index
Lagrangian Submanifold
Lagrangian Subspaces
Linear Hamiltonian System
maslov
Maslov index
Morse Index
Non-degenerate Critical Point
Non-degenerate Systems
operator
orthogonal
periodic orbits
Periodic Points
Self-adjoint Operator
Self-adjoint Realization
solutions
space
Standard Symplectic Form
superquadratic dynamics
Symplectic Manifold
Symplectic Matrices
Symplectic Matrix
symplectic topology
t-periodic
T-periodic Solutions
Time Dependent Vector Field
variational methods
Product details
- ISBN 9781138417588
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 04 Apr 2018
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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.
