| Introduction | p. 1 |
| Fall from Paradise | p. 1 |
| Billiards and Broken Geodesics | p. 4 |
| An Ancestor of Symplectic Topology | p. 8 |
| Twist Maps of the Annulus | p. 11 |
| Monotone Twist Maps of the Annulus | p. 11 |
| Generating Functions and Variational Setting | p. 17 |
| Examples | p. 21 |
| The Poincare-Birkhoff Theorem | p. 27 |
| The Aubry-Mather Theorem | p. 31 |
| Introduction | p. 31 |
| Cyclically Ordered Sequences And Orbits | p. 34 |
| Minimizing Orbits | p. 36 |
| CO Orbits Of All Rotation Numbers | p. 40 |
| Aubry-Mather Sets | p. 41 |
| Appendix: Cyclically Ordered Sequences and Circle Maps | p. 46 |
| Ghost Circles | p. 53 |
| Gradient Flow of the Action | p. 54 |
| The Gradient Flow and the Aubry-Mather Theorem | p. 57 |
| Ghost Circles | p. 59 |
| Construction of Ghost Circles | p. 63 |
| Construction of Disjoint Ghost Circles | p. 67 |
| Proof of Lemma 18.5 | p. 70 |
| Proof of Theorem 18.1 | p. 73 |
| Remarks and Applications | p. 78 |
| Proofs of Monotonicity and of the Sturmian Lemma | p. 82 |
| Symplectic Twist Maps | p. 87 |
| Symplectic Twist Maps of T[superscript n] x [actual symbol not reproducible][superscript n] | p. 88 |
| Examples | p. 91 |
| More on Generating Functions | p. 95 |
| Symplectic Twist Maps on General Cotangent Bundles of Compact Manifolds | p. 99 |
| Periodic Orbits for Symplectic Twist Maps of T[superscript n] x [actual symbol not reproducible][superscript n] | p. 103 |
| Presentation Of The Results | p. 103 |
| Finite Dimensional Variational Setting | p. 107 |
| Second Variation and Nondegenerate Periodic Orbits | p. 110 |
| The Coercive Case | p. 112 |
| Asymptotically Linear Systems | p. 114 |
| Ghost Tori | p. 116 |
| Hyperbolicity Vs. Action Minimizers | p. 118 |
| Invariant Manifolds | p. 123 |
| The Theory of Kolmogorov-Arnold-Moser | p. 123 |
| Properties of Invariant Tori | p. 127 |
| (Un)Stable Manifolds and Heteroclinic orbits | p. 135 |
| Instability, Transport and Diffusion | p. 141 |
| Hamiltonian Systems vs. Twist Maps | p. 145 |
| Case Study: The Geodesic Flow | p. 146 |
| Decomposition of Hamiltonian Maps into Twist Maps | p. 154 |
| Return Maps in Hamiltonian Systems | p. 164 |
| Suspension of Symplectic Twist Maps by Hamiltonian Flows | p. 165 |
| Periodic Orbits for Hamiltonian Systems | p. 173 |
| Periodic Orbits in the Cotangent of the n-Torus | p. 174 |
| Periodic Orbits in General Cotangent Spaces | p. 177 |
| Linking of Spheres | p. 186 |
| Generalizations of the Aubry-Mather Theorem | p. 191 |
| Theory for Functions on Lattices and PDE's | p. 192 |
| Monotone Recurrence Relationst | p. 196 |
| Anti-Integrable Limit | p. 197 |
| Mather's Theory of Minimal Measures | p. 199 |
| The Case of Hyperbolic Manifolds | p. 212 |
| Concluding Remarks | p. 216 |
| Generating Phases and Symplectic Topology | p. 217 |
| Chaperon's Method and the Theorem Of Conley-Zehnder | p. 218 |
| Generating Phases and Symplectic Geometry | p. 224 |
| Overview of Symplectic Geometry | p. 233 |
| Symplectic Vector Spaces | p. 233 |
| Subspaces of a Symplectic Vector Space | p. 236 |
| Symplectic Linear Maps | p. 238 |
| Symplectic Manifolds | p. 241 |
| Cotangent Bundles | p. 243 |
| Hamiltonian Systems | p. 247 |
| Some Topological Tools | p. 259 |
| Hands on Introduction to Homology Theory | p. 260 |
| Morse Theory | p. 267 |
| Controlling the Topology of Invariant Sets | p. 273 |
| Topological Proofs | p. 276 |
| Generating Phases Quadratic at Infinity | p. 284 |
| Covering Spaces, Lifts and Fundamental Group | p. 288 |
| Bibliography | p. 293 |
| Index | p. 303 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
