Author | Hofer, Helmut. author |
---|---|
Title | Symplectic Invariants and Hamiltonian Dynamics [electronic resource] / by Helmut Hofer, Eduard Zehnder |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1994 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8540-9 |
Descript | XIII, 346 p. 2 illus. online resource |
1 Introduction -- 1.1 Symplectic vector spaces -- 1.2 Symplectic diffeomorphisms and Hamiltonian vector fields -- 1.3 Hamiltonian vector fields and symplectic manifolds -- 1.4 Periodic orbits on energy surfaces -- 1.5 Existence of a periodic orbit on a convex energy surface -- 1.6 The problem of symplectic embeddings -- 1.7 Symplectic classification of positive definite quadratic forms -- 1.8 The orbit structure near an equilibrium, Birkhoff normal form -- 2 Symplectic capacities -- 2.1 Definition and application to embeddings -- 2.2 Rigidity of symplectic diffeomorphisms -- 3 Existence of a capacity -- 3.1 Definition of the capacity c0 -- 3.2 The minimax idea -- 3.3 The analytical setting -- 3.4 The existence of a critical point -- 3.5 Examples and illustrations -- 4 Existence of closed characteristics -- 4.1 Periodic solutions on energy surfaces -- 4.2 The characteristic line bundle of a hypersurface -- 4.3 Hypersurfaces of contact type, the Weinstein conjecture -- 4.4 โClassicalโ Hamiltonian systems -- 4.5 The torus and Hermanโs Non-Closing Lemma -- 5 Compactly supported symplectic mappings in ?2n -- 5.1 A special metric d for a group D of Hamiltonian diffeomorphisms -- 5.2 The action spectrum of a Hamiltonian map -- 5.3 A โuniversalโ variational principle -- 5.4 A continuous section of the action spectrum bundle -- 5.5 An inequality between the displacement energy and the capacity -- 5.6 Comparison of the metric d on D with the C0-metric -- 5.7 Fixed points and geodesics on D -- 6 The Arnold conjecture, Floer homology and symplectic homology -- 6.1 The Arnold conjecture on symplectic fixed points -- 6.2 The model case of the torus -- 6.3 Gradient-like flows on compact spaces -- 6.4 Elliptic methods and symplectic fixed points -- 6.5 Floerโs appraoch to Morse theory for the action functional -- 6.6 Symplectic homology -- A.2 Action-angle coordinates, the Theorem of Arnold and Jost -- A.4 The Cauchy-Riemann operator on the sphere -- A.5 Elliptic estimates near the boundary and an application -- A.6 The generalized similarity principle -- A.7 The Brouwer degree -- A.8 Continuity property of the Alexander-Spanier cohomology