Hamiltonian Systems with Three or More Degrees of Freedom

Front Matter....Pages i-xxiv
Front Matter....Pages 1-1
Inflection Points, Extatic Points and Curve Shortening....Pages 3-10
Topologically Necessary Singularities on Moving Wavefronts and Caustics....Pages 11-12
Heteroclinic Chains of Skew Product Hamiltonian Systems....Pages 13-25
Order and Chaos in 3-D Systems....Pages 26-38
Splitting of Separatrices in Hamiltonian Systems and Symplectic Maps....Pages 39-54
On The Discrete One-Dimensional Quasi-Periodic Schrödinger Equation and Other Smooth Quasi-Periodic Skew Products....Pages 55-61
Lindstedt Series and Kolmogorov Theorem....Pages 62-71
A Classical Self-Contained Proof of Kolmogorov’s Theorem on Invariant Tori....Pages 72-89
Dynamical Stability in Lagrangian Systems....Pages 90-114
The Origin of Chaotic Behaviour in the Kirkwood Gaps....Pages 115-125
Examples of Compact Hypersurfaces in R 2P , 2P ≥ 6, With No Periodic Orbits....Pages 126-126
Hamiltonian Systems with Three Degrees of Freedom and Hydrodynamics....Pages 127-133
Introduction to Frequency Map Analysis....Pages 134-150
Lindstedt Series for Lower Dimensional Tori....Pages 151-167
Arnold Diffusion; a Compendium of Remarks and Questions....Pages 168-183
Old and New Applications of Kam Theory....Pages 184-192
On Adiabatic Invariance in Two-Frequency Systems....Pages 193-212
The Method of Rational Approximations: Theory and Applications....Pages 213-222
Dynamical Systems Methods for Space Missions on a Vicinity of Collinear Libration Points....Pages 223-241
A Mechanism of Ergodicity in Standard-Like Maps....Pages 242-243
Front Matter....Pages 1-1
Continuous Averaging in Hamiltonian Systems....Pages 244-253
Phase Space Geometry and Dynamics Associated with the 1:2:2 Resonance....Pages 254-269
From Singular Point Analysis to Rigorous Results on Integrability: a Dream of S. Kowalevskaya....Pages 270-282
Front Matter....Pages 283-283
Time Singularities for Polynomial Hamiltonians with Analytic Time Dependence....Pages 285-289
Numerical Study of Turbulence in N-Body Hamiltonian Systems with Long Range Force: I. Relaxation....Pages 290-294
Phase Space Structures in 3 and 4 Degrees of Freedom: Application to Chemical Reactions....Pages 295-299
Modulated Diffusion for Symplectic Maps....Pages 300-304
On The Jeans-Landau-Teller Approximation for Adiabatic Invariants....Pages 305-309
Periodic Orbits and Quantum Mechanics of Molecular Hamiltonian Systems....Pages 310-313
Chaos in Atom-Surface Collisions....Pages 314-317
On The Non-Integrability of the Mixmaster Universe Model....Pages 318-323
Branching of Solutions as Obstruction to the Existence of a Meromorphic Integral in Many-Dimensional Systems....Pages 324-329
The Energy Surfaces of the Kovalevskaya-Top....Pages 330-334
Filling Rates for Linear Flow on the Torus: Recent Progress and Applications....Pages 335-339
Invariant Spectra of Orbits in Multidimensional Symplectic Maps....Pages 340-344
On the Convergence of Formal Series Containing Small Divisors....Pages 345-349
Systems with an Invariant Measure on Lie Groups....Pages 350-356
Stochasticity of the 2/1 Asteroidal Resonance: a Symplectic Mapping Approach....Pages 357-361
On Perturbed Oscillators in1–1–1 Resonance: Critical Inclination in the 3D Hénon-Heiles Potential....Pages 362-366
Splitting of Separatrices for (Fast) Quasiperiodic Forcing....Pages 367-371
Front Matter....Pages 283-283
A Possible Mechanism for the Kam Tori Breakdown....Pages 372-376
On the Dynamics Near Resonant Equilibria....Pages 377-385
Exponentially Small Estimates for Kam Theorem Near an Elliptic Equilibrium Point....Pages 386-390
Fast Diffusion and Universality Near Intersecting Resonances....Pages 391-397
Quasi-Periodic Motion of a Rigid Body Under Weak Forces....Pages 398-402
Center and Center-(Un)Stable Manifolds of Elliptic-Hyperbolic Fixed Points of 4 D -Symplectic Maps. an Example: the Froeschlé Map....Pages 403-407
A Many-Particle Adiabatic Invariant....Pages 408-412
The Non-Integrability of Perturbed Hamiltonians of N Degrees of Freedom and the Continuation of Periodic Orbits....Pages 413-417
Structure of the 5-Dimensional Manifold of Constant Energy in the J 2 -Problem....Pages 418-421
The Bifurcations of the Langmuir Orbit in the Two-Electron Atom....Pages 422-425
Domains of Convergence of Kam Type Iterations for Eigenvalue Problems....Pages 426-429
Nonlinear Dynamics in an Extended Neighbourhood of the Translunar Equilibrium Point....Pages 430-434
Analysis of Quantum Eigenstates in a 3-Mode System....Pages 435-439
Detection of Stable Manifolds in High Dimensional Phase Space....Pages 440-443
Ordered Motion in Hamiltonian Systems with Many Degrees of Freedom....Pages 444-448
Some Relations from Hamiltonian Mechanics and their Applications to Plasma Physics....Pages 449-452
Effective Stability in Reversible Systems....Pages 453-457
New Criterion of Nonintegrability for an N -Degrees-of-Freedom Hamiltonian System....Pages 458-470
The Invariant Measure for the Satellite Ground Station View Period Problem....Pages 471-474
The two Rigid Bodies Problem. Reduction and Relative Equilibria....Pages 475-479
Front Matter....Pages 283-283
Transition Orbits and Transition Times Along Chains of Hyperbolic Tori....Pages 480-484
Persistence of Asteroids After a Close Encounter....Pages 485-488
Structure of the Sets of Invariant Tori and Problems of Stability in Reversible Systems....Pages 489-493
On the Break-Up of Invariant Tori with three Frequencies....Pages 494-498
The Arnol’d Web in Atomic Physics....Pages 499-503
Psi-Series, Singularities of Solutions and Integrability of Polynomial Systems....Pages 504-508
Galoisian Obstructions to Integrability of Hamiltonian Systems: Statements and Examples....Pages 509-513
Bounds on Diffusion in Phase Space: Connection Between Nekhoroshev and Kam Theorems and Superexponential Stability of Invariant Tori....Pages 514-517
Bifurcation at Complex Instability....Pages 518-522
Global Dynamics of a Galactic Potential via Frequency Map Analysis....Pages 523-527
A Particular Class of Integrable Connection....Pages 528-532
Poincaré-Melnikov-Arnold Method for Twist Maps....Pages 533-537
Transport in a Class of N -D.O.F. Systems....Pages 538-543
Mel’nikov Vector and Singularity Analysis of Periodically Perturbed 2 D.O.F Hamiltonian Systems....Pages 544-548
A Study of Reduced Action-Functional for the Newtonian 3-Body Problem....Pages 549-553
Satellite Dynamics About Asteroids: Computing Poincaré Maps for the General Case....Pages 554-557
Mel’nikov Analysis of a Hamiltonian Perturbation of the Nonlinear Schrödinger Equation....Pages 558-562
First Order Adiabatic Approximation for a Class of Classical Slow-Fast Systems with Ergodic Fast Dynamics....Pages 563-567
The Lack-of-Parameters Problem in the Kam Theory Revisited....Pages 568-572
Homoclinic Invariant for the Coupled Standard Map....Pages 573-577
Front Matter....Pages 283-283
Destruction of Adiabatic Invariants on Resonances: Example from the Rigid Body Dynamics....Pages 578-582
Numerical Study of the Phase Space of a four Dimensional Symplectic Map....Pages 583-587
Caustics, Cusps and Chaos in Hamiltonian Systems....Pages 588-591
A Homoclinic Orbit for the Double Pendulum....Pages 592-594
Some Bifurcations Related to Homoclinic Tangencies for 1-Parameter Families of Symplectic Diffeomorphisms....Pages 595-599
Resonant Normal forms for four Dimensional Symplectic Mappings and Applications to Nonlinear Beam Dynamics....Pages 600-604
Approximation of Invariant Surfaces by Periodic Orbits in High-Dimensional Maps....Pages 605-609
Exponential Asymptotics and Approximation of Stable and Unstable Manifolds in Singularly Perturbed Nonlinear Systems....Pages 610-613
Singularity Analysis Towards Nonintegrability of Nonhomogeneous Nonlinear Lattices....Pages 614-617
Adiabatic Chaos of Streamlines in a Family of 3 D Confined Stokes Flows....Pages 618-624
Toda Lattices on Finite Symmetric Space Graphs....Pages 625-627
Effective Stability Around Periodic Orbits of the Spatial RTBP....Pages 628-632
On the Computation of Periodic Orbits and Invariant Surfaces of 4 D -Symplectic Mappings....Pages 633-637
On the Computation of all the Equilibrium Points in Hamiltonian Systems with Three Degrees of Freedom....Pages 638-641
A Method for Computing Families of Periodic Orbits Based on Unconstrained Optimization....Pages 642-645
Phase Space Geometry of Reactive Scattering....Pages 646-648
Numerical Construction of the Poincaré Map, with Application to Accelerators....Pages 649-653
Back Matter....Pages 654-658