Hamiltonian Mechanics: Integrability and Chaotic Behavior

Front Matter....Pages i-x
Non-Integrability Criterion of Hamiltonian Systems based on Ziglin’s Theorem and its Relation to the Singular Point Analysis....Pages 1-12
Averaging under Fast Quasiperiodic Forcing....Pages 13-34
Natural Boundaries of Normalizing Transformations....Pages 35-42
Singular Perturbation in Hamiltonian Mechanics....Pages 43-49
The Structure of Chaos....Pages 51-71
From Integrability to Chaos: Examples of Interrelations between Physics and Dynamics for Minor Bodies in the Solar System....Pages 73-88
Successive Elimination of Harmonics: A way to Explore the Resonant Structure of a Hamiltonian System....Pages 89-101
Periodic Solutions of Nonlinear Schrödinger Equations and the Nash-Moser Method....Pages 103-122
On the Tendency Toward Ergodicity with Increasing Number of Degrees of Freedom in Hamiltonian Systems....Pages 123-129
Gibbsian Check of the Validity of Gibbsian Calculation through Dynamical Observables....Pages 131-138
Adiabatic Invariants and Time Scales for Energy Sharing in Models of Classical Gases....Pages 139-151
Numerical Integration of Hamiltonian Systems in the Presence of Additional Integrals: Application of the Observer Method....Pages 153-165
Symmetries and Topology of Dynamical Systems with two Degrees of Freedom....Pages 167-172
Variational Criteria for Nonintegrability and Chaos in Hamiltonian Systems....Pages 173-179
Exponentially Small Splitting in Hamiltonian Systems....Pages 181-187
Integrable and Chaotic Behaviour in the Paul Trap and the Hydrogen Atom in a Generalized van der Waals Potential....Pages 189-196
Recent Applications of Hamiltonian Dynamics to Accelerator Physics....Pages 197-204
Singularity Analysis of 2D Complexified Hamiltonian Systems....Pages 205-212
Perturbation Theory for Systems without Global Action-Angle Coordinates....Pages 213-220
A Non-Integrability Test for Perturbed Hamiltonian Systems of Two Degrees of Freedom....Pages 221-228
Librational Invariant Surfaces in the Spin-Orbit Problem....Pages 229-235
Normalization of Resonant Hamiltonians....Pages 237-244
Effective Stability for Periodically Perturbed Hamiltonian Systems....Pages 245-252
Bihamiltonian Systems and Lax Representation....Pages 253-259
An Efficient Method for Computing Periodic Orbits of Conservative Dynamical Systems....Pages 261-274
The Dynamics of Trace Maps....Pages 275-285
Scars in Groups of Eigenfunctions....Pages 287-294
A model of Poincaré and Rigorous Proof of the Second Element of Thermodynamics from Mechanics....Pages 295-297
Nekhoroshev and KAM Theorems Revisited via a Unified Approach....Pages 299-306
Dynamics and K-Symmetries....Pages 307-314
Quantal-Classical Mixed mode Dynamics of Coupled Oscillators....Pages 315-320
The three-wave Interaction of four waves Revisited: A Lax Pair and Possibly General Solution....Pages 321-328
Chaotic Friedman-Robertson-Walker Cosmology Coupled to a Real Free Massive Scalar Field in Maupertuis Picture....Pages 329-333
The Method of Modular Smoothing....Pages 335-340
Soliton Chaos in Elastic Chains and Turbulence....Pages 341-344
Stochastic webs with Fourfold Rotation Symmetry....Pages 345-352
Antibrackets and Supersymmetric Mechanics....Pages 353-360
Integrable Systems and Confocal Quadrics....Pages 361-369
An Elementary approach to Integrability Condition for the Euler Equations on Lie Algebra so(4)....Pages 371-376
Integrable Hamiltonian Systems and Poisson Actions with Simple Singular Points....Pages 377-384
Dynamics and Bifurcations in Two-Parameter Unfolding of a Hamiltonian System with a Homoclinic Orbit to a Saddle-Center....Pages 385-390
Self-Similar Isomonodromy Solutions of Nonlinear Schrödinger Equation....Pages 391-398
A method for Visualizing the 4-Dimensional Space of Section in 3-D Hamiltonian Systems....Pages 399-403
Non-Adiabatic Aspects of Time-Dependent Hamiltonian Systems....Pages 405-411
A Study of a Finite-Dimensional Dynamical System Approximating the Evolution of Quantum Averages....Pages 413-420
Back Matter....Pages 421-422