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The Dynamical Behaviour of Our Planetary System

It is now a well established tradition that every four years, at the end of winter, a group of "celestial mechanicians" from all over the world gather at the "Alpen- gasthof Peter Rosegger" in the Styrian Alps (Ramsau, Austria). This time the colloquium was held from March 17 to March 23, 1996 and was devoted to the Dynamical Behaviour of our Planetary System. The papers covered a large range of questions of current interest: theoretical questions (re- nances, universal properties, non integrability, transport, ... ) and questions about numerical tools ( symplectic maps, indicators of chaos, ... ) were particularly well represented; the never ending problem of the sculpting of the asteroid belt was also qui te popular. You will find in the following pages a pot-pourri of what we listen to; you will miss of course the diversity of accents with which the tunes were delivered: from China, from Japan, from Brazil, from the United-States of America and from all over Europe, East and West. Let us not forget that the comet 199682 (Hyakutake) came to visit us; many an evening was spent on the deck of the Alpengasthof contemplating this celestial visitor who liked to play hide-and-seek behind the spruce trees.
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Table of Contents

Preface. Theoretical Dynamics. Scattering by Resonances; A. Neishtadt. Non-Integrability in Hamiltonian Mechanics; S. Ichtiaroglou. Regular and Irregular Periodic Orbits; G. Contopoulos, E. Grousouzakou. Universal Properties of Escape in Dynamical Systems; C. Siopis, et al. Numerical Methods of Analysis. Mapping and Dynamical Systems; M. Sidlichovsky. A New Fast Fourier Method for Evaluating Fourier Spectra at Arbitrary Frequencies; K. Wodnar. Planets and Satellites. On the Use of Analytical Theories in the Calculation of Precession-Nutation; P. Bretagnon. Asteroids. The Nekhoroshev Theorem and the Asteroid Belt Dynamical System; A. Morbidelli, M. Guzzo. Frequency Modified Fourier Transform and its Application to Asteroids; M. Sidlichovsky, D. Nesvorny. The Trojan Problem; B. Erdi. Dynamical Transport to Planet-Crossing Orbits; Ch. Froeschle. Review of the Dynamics in the Kirkwood Gaps; M. Moons. Miscellaneous. Open Problems on the Eve of the Next Millennium; V. Szebehely. Limit of Comprehension, Reference Frames and General Relativity; H. Eichhorn. Theoretical Dynamics. Stable Chaos: A First Model; A. Lemaitre. Transport in Perturbed Integrable Hamiltonian Systems and the Fractality of Phase Space; H. Varvoglis, et al. Equilibria Bifurcations of Satellite Orbits; V.W. Kudielka. Numerical Methods of Analysis. Fast Lyapunov Indicators. Comparison with Other Chaos Indicators. Application to Two and Four Dimensional Maps; E. Lega, C. Froeschle. Asteroid Motion near the 2:1 Resonance: A Symplectic Mapping Approach; J. Hadjidemetriou, A. Lemaitre. Symplectic Integrators for Hill's LunarProblem; J. Waldvogel. Rotation Number and Global Stability of Symplectic Integrator; Yi-Sui Sun, Ji-Lin Zhou. Planets and Satellites. On a Global Expansion of the Planar Disturbing Function; C. Beauge. Links Between Time Scales Using Barycentric Relativistic Ephemerides; X. Moisson. Orbital Stability of Planetary Quasi-Satellites; S. Mikkola, K. Innanen. Alternative Derivations of Perturbations with Use of a Mixed Reference-Plane System: Application to the Motion of the Orbit Plane of Hyperion; P.J. Message. Astrodynamic Study of the Earth Rotation; C. Marchal. Asteroids. Orbital Evolution of Asteroids in the Hecuba Gap; S. Ferraz-Mello, T.A. Michtchenko. A Study of the Local Lyapunov Numbers for Orbits in the Outer Solar System; E. Lohinger. Miscellaneous. On the Influence of Supernova Shockfronts on the Stability of the Solar System; W. Schaffenberger, A. Hanslmeier. Henri Poincare: A Decisive Contribution to Special Relativity; C. Marchal. Periodic Orbits in the Sitnikov Problem; J. Kallrath, et al.

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