Hamiltonian dynamical systems : a reprint selection

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 12
Part 1: Introductory Articles......Page 14
 Survey of Hamiltonian Dynamics......Page 16
 Is the Solar System Stable?......Page 33
 Regular and Irregular Motion......Page 40
 The Mechanisms of Stochasticity in Classical Dynamical Systems......Page 67
Part 2: Equilibria and Periodic Orbits......Page 88
 Lectures on Hamiltonian Systems......Page 90
 Stability of Equilibria of Hamiltonian Systems......Page 150
 On the Periodic Motions of Dynamical Systems......Page 167
 Linear Stability of Periodic Orbits in Lagrangian Systems......Page 188
 Generic Bifurcation of Periodic Points......Page 191
 Universal Behaviour in Families of Area-Preserving Maps......Page 204
 Quasi-Elliptic Periodic Points in Conservative Dynamical Systems......Page 223
Part 3: Quasiperiodic Orbits......Page 250
 Geodesics on a Two-Dimensional Riemannian Manifold with Periodic Coefficients......Page 252
 Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics......Page 273
 Variational Principles for Invariant Tori and Cantori......Page 380
 Periodic and Quasi-Periodic Orbits for Twist Maps......Page 389
 Non-Existence of Invariant Circles......Page 408
Part 4: Breakup of Invariant Tori......Page 418
 Resonance Processes in Magnetic Traps......Page 420
 Destruction of Magnetic Surfaces by Magnetic Field Irregularities......Page 428
 A Method for Determining a Stochastic Transition......Page 432
 Fractal Diagrams for Hamiltonian Stochasticity......Page 451
 Large-Scale Stochasticity in Hamiltonian Systems......Page 459
 A Renormalisation Approach to Invariant Circles in Area-Preserving Maps......Page 475
Part 5: Chaotic Behaviour......Page 494
 Roughness of Geodesic Flows on Compact Riemannian Manifolds of Negative Curvature......Page 496
 Ergodic Properties of Geodesic Flows on Closed Riemannian Manifolds of Negative Curvature......Page 499
 Markov Partitions and C-Diffeomorphisms......Page 503
 Ljapunov Characteristic Exponents and Ergodic Properties of Smooth Dynamical Systems with an Invariant Measure......Page 525
 Ergodicity of Linked Twist Maps......Page 529
 Principles for the Design of Billiards with Nonvanishing Lyapunov Exponents......Page 544
 Shift Automorphisms in the Hénon Mapping......Page 568
Part 6: Mixed Systems......Page 580
 A Model Problem with the Coexistence of Stochastic and Integrable Behaviour......Page 582
 Fat Fractals on the Energy Surface......Page 594
 Long-Time Correlations in the Stochastic Regime......Page 598
 Transport in Hamiltonian Systems......Page 619
 Instability of Dynamical Systems with Several Degrees of Freedom......Page 646
 Behavior of Hamiltonian Systems Close to Integrable......Page 651
 Melnikov’s Method and Arnold Diffusion for Perturbations of Integrable Hamiltonian Systems......Page 653
 Arnold Diffusion, Ergodicity and Intermittency in a Coupled Standard Mapping......Page 660
Part 7: Applications......Page 666
 Nature of the Kirkwood Gaps in the Asteroid Belt......Page 668
 The Chaotic Rotation of Hyperion......Page 673
 A Method for Mapping a Toroidal Magnetic Field by Storage of Phase Stabilized Electrons......Page 689
 Electron Heat Transport in a Tokamak with Destroyed Magnetic Surfaces......Page 697
 Elimination of Stochasticity in Stellerators......Page 701
 The Dynamics of the Beam-Beam Interaction......Page 704
 Intramolecular Dynamics and Nonlinear Mechanics of Model OCS......Page 723
 Stirring by Chaotic Advection......Page 738
 The Twist Map, The Extended Frenkel-Kontorova Model and the Devil’s Staircase......Page 759
Part 8: Bibliography......Page 778
 References......Page 780