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Hamiltonian Mechanics : Integrability and Chaotic Behavior - John Seimenis

Hamiltonian Mechanics

Integrability and Chaotic Behavior

By: John Seimenis (Editor)


Published: 31st December 1994
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This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.

Non-integrability criterion of Hamiltonian systems based on Ziglin's Theorem and its relation to the singular point analysisp. 1
Averaging under fast quasiperiodic forcingp. 13
Natural boundaries of normalizing transformationsp. 35
Singular perturbation in Hamiltonian Mechanicsp. 43
The structure of Chaosp. 51
From Integrability to Chaos: Examples of interrelations between physics and dynamics for minor bodies in the solar systemp. 73
Successive elimination of harmonics: A way to explore the resonant structure of a Hamiltonian systemp. 89
Periodic solutions of nonlinear Schrodinger equations and the Nash-Moser methodp. 103
On the tendency toward ergodicity with increasing number of degrees of freedom in Hamiltonian systemsp. 123
Gibbsian check of the validity of Gibbsian calculation through dynamical observablesp. 131
Adiabatic invariants and time scales for energy sharing in models of classical gasesp. 139
Numerical integration of Hamiltonian systems in the presence of additional integrals: Application of the observer methodp. 153
Symmetries and topology of dynamical systems with two degrees of freedomp. 167
Variational criteria for nonintegrability and chaos in Hamiltonian systemsp. 173
Exponentially small splitting in Hamiltonian systemsp. 181
Integrable and chaotic behaviour in the Paul trap and the hydrogen atom in a generalized van der Waals potentialp. 189
Recent applications of Hamiltonian dynamics to accelerator physicsp. 197
Singularity analysis of 2D complexified Hamiltonian systemsp. 205
Perturbation theory for systems without global action-angle coordinatesp. 213
A non-integrability test for perturbed Hamiltonian systems of two degrees of freedomp. 221
Librational invariant surfaces in the spin-orbit problemp. 229
Normalization of resonant Hamiltoniansp. 237
Effective stability for periodically perturbed Hamiltonian systemsp. 245
Bihamiltonian systems and Lax representationp. 253
An efficient method for computing periodic orbits of conservative dynamical systemsp. 261
The dynamics of trace mapsp. 275
Scars in groups of eigenfunctionsp. 287
A model of Poincare and rigorous proof of the second element of thermodynamics from mechanicsp. 295
Nekhoroshev and KAM theorems revisited via a unified approachp. 299
Dynamics and k-symmetriesp. 307
Quantal-classical mixed mode dynamics of coupled oscillatorsp. 315
The three-wave interaction of four waves revisited: A Lax pair and possibly general solutionp. 321
Chaotic Friedman-Robertson-Walker Cosmology coupled to a real free massive scalar field in Maupertuis picturep. 329
The method of modular smoothingp. 335
Soliton chaos in elastic chains and turbulencep. 341
Stochastic webs with fourfold rotation symmetryp. 345
Antibrackets and supersymmetric Mechanicsp. 353
Integrable systems and confocal quadricsp. 361
An elementary approach to integrability condition for the Euler equations on Lie algebra so(4)p. 371
Integrable Hamiltonian systems and Poisson actions with simple singular pointsp. 377
Dynamics and bifurcations in two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-centerp. 385
Self-similar isomonodromy solutions of nonlinear Schrodinger equationp. 391
A method for visualizing the 4-dimensional space of section in 3-D Hamiltonian systemsp. 399
Non-adiabatic aspects of time-dependent Hamiltonian systemsp. 405
A study of a finite-dimensional dynamical system approximating the evolution of quantum averagesp. 413
Indexp. 421
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306448089
ISBN-10: 0306448084
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 422
Published: 31st December 1994
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 26.67 x 17.78  x 3.18
Weight (kg): 0.95