Hamiltonian Mechanics

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.

Zusammenfassung
Proceedings of a NATO ARW held in Torun, Poland, June 28-July 2, 1993

Inhalt
Invited papers.- Non-integrability criterion of Hamiltonian systems based on Ziglin's Theorem and its relation to the singular point analysis.- Averaging under fast quasiperiodic forcing.- Natural boundaries of normalizing transformations.- Singular perturbation in Hamiltonian Mechanics.- The structure of Chaos.- From Integrability to Chaos: Examples of interrelations between physics and dynamics for minor bodies in the solar system.- Successive elimination of harmonics: A way to explore the resonant structure of a Hamiltonian system.- Periodic solutions of nonlinear Schrodinger equations and the Nash-Moser method.- On the tendency toward ergodicity with increasing number of degrees of freedom in Hamiltonian systems.- Gibbsian check of the validity of Gibbsian calculation through dynamical observables.- Adiabatic invariants and time scales for energy sharing in models of classical gases.- Numerical integration of Hamiltonian systems in the presence of additional integrals: Application of the observer method.- Symmetries and topology of dynamical systems with two degrees of freedom.- Contributed papers.- Variational criteria for nonintegrability and chaos in Hamiltonian systems.- Exponentially small splitting in Hamiltonian systems.- Integrable and chaotic behaviour in the Paul trap and the hydrogen atom in a generalized van der Waals potential.- Recent applications of Hamiltonian dynamics to accelerator physics.- Singularity analysis of 2D complexified Hamiltonian systems.- Perturbation theory for systems without global action-angle coordinates.- A non-integrability test for perturbed Hamiltonian systems of two degrees of freedom.- Librational invariant surfaces in the spin-orbit problem.- Normalization of resonant Hamiltonians.- Effective stability for periodicallyperturbed Hamiltonian systems.- Bihamiltonian systems and Lax representation.- An efficient method for computing periodic orbits of conservative dynamical systems.- The dynamics of trace maps.- Scars in groups of eigenfunctions.- A model of Poincaré and rigorous proof of the second element of thermodynamics from mechanics.- Nekhoroshev and KAM theorems revisited via a unified approach.- Dynamics and k-symmetries.- Quantal-classical mixed mode dynamics of coupled oscillators.- The three-wave interaction of four waves revisited: A Lax pair and possibly general solution.- Chaotic Friedman-Robertson-Walker Cosmology coupled to a real free massive scalar field in Maupertuis picture.- The method of modular smoothing.- Soliton chaos in elastic chains and turbulence.- Stochastic webs with fourfold rotation symmetry.- Antibrackets and supersymmetric Mechanics.- Integrable systems and confocal quadrics.- An elementary approach to integrability condition for the Euler equations on Lie algebra so(4).- Integrable Hamiltonian systems and Poisson actions with simple singular points.- Dynamics and bifurcations in two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center.- Self-similar isomonodromy solutions of nonlinear Schrödinger equation.- A method for visualizing the 4-dimensional space of section in 3-D Hamiltonian systems.- Non-adiabatic aspects of time-dependent Hamiltonian systems.- A study of a finite-dimensional dynamical system approximating the evolution of quantum averages.