Index Theory for Symplectic Paths with Applications

摘要: I The Symplectic Group Sp(2n).- 1 Algebraic Aspects.- 1.1 matrices.- 1.2 spaces.- 1.3 Eigenvalues of symplectic 1.4 Normal forms for the eigenvalue 1.- 1.5 ?1.- 1.6 eigenvalues in U?R.- 1.7 outside U.- 1.8 Basic normal forms.- 1.9 Perturbations basic 2 Topological 2.1 Structures Sp(2) and its subsets.- 2.2 global structure Sp(2n,R).- 2.3 Hyperbolic matrix set.- 2.4 Structure regular sets.- 2.5 singular 2.6 Transversality rotation paths.- 2.7 Orientability M?,(2n) II Variational Method.- 3 Hamiltonian Systems Canonical Transformations.- 3.1 transformations.- 3.2 Generating functions.- 4 Functional.- 4.1 Galerkin approximation.- 4.2 L2-Variational Structure.- 4.3 saddle point reduction.- 4.4 dimension theorem on kernels.- 4.5 Certain estimates.- III Index Theory.- 5 Functions Paths.- 5.1 Paths Sp(2).- 5.2 Non-degenerate paths 5.3 properties non-degenerate 5.4 degenerate 6 Properties Functions.- 6.1 functions Morse indices.- 6.2 An axiom approach further properties.- 7 Relations with other Indices.- 7.1 7.2 Second order systems.- 7.3 Lagrangian IV Iteration 8 Precise Formulae.- 8.1 8.2 elliptic 8.3 General 9 Bott-type 9.1 Splitting numbers.- 9.2 formulae.- 9.3 Abstract precise iteration 10 Inequalities.- 10.1 Estimates via mean index initial index.- 10.2 Successive 10.3 Controlling numbers 11 Common Jump Theorem.- 11.1 A common selection theorem.- 11.2 jump 12 Theory Closed Geodesics.- 12.1 theory.- 12.2 V Applications.- 13 Rabinowitz Conjecture.- 13.1 Minimax principle preparations.- 13.2 minimal period 13.3 Asymptotically linear 13.4 Superquadratic 13.5 13.6 Subharmonics.- 13.7 Notes comments.- 14 Periodic Orbits Tori.- 14.1 Critical module 14.2 finite energy homology 14.3 modules isomorphisms.- 14.4 Global homological injectivity.- 14.5 vanishing.- 14.6 15 Characteristics Convex Hypersurfaces.- 15.1 dual action principle.- 15.2 15.3 orbits jumps.- 15.4 Existence multiplicity.- 15.5 Stability results.- 15.6 Symmetric hypersurfaces.- 15.7 comments.