Ergodic Concepts in Stellar Dynamics Proceedings of an International Workshop Held at Geneva Observatory University of Geneva, Switzerland, 1{u2013}3 March 1993

Advances in the dynamics of stellar systems have been made recently by applying mathematical methods of ergodic theory and chaotic dynamics, by numerous computer simulations, and by observations with the most powerful telescopes. This has led to a considerable change of our view on stellar systems. These systems appear much more chaotic than was previously thought and subject to various instabilities leading to new paths of evolution than previously thought. The implications are fundamental for our views on the evolution of the galaxies and the universe. Such questions are addressed in this book, especially in the 8 review papers by leading experts on various aspects of the N-body problem, explaining at the graduate/postgraduate level the concepts, methods, techniques and results. Structural and dynamical forms of elliptical and dwarf galaxies....Pages 3-21 Some clues about the dynamics of globular clusters from high-resolution observation....Pages 22-33 Diffusion of stellar orbits in the galactic disk....Pages 34-40 Ergodic methods in stellar dynamics....Pages 41-55 On a notion of weak stability and its relevance for celestial mechanics and molecular dynamics....Pages 56-63 Recent developments in the dynamics of nonlinear Hamiltonian systems with many degrees of freedom....Pages 64-84 Numerical exploration of the circular billiard with gravity....Pages 85-90 Ergodicity and mixing in gravitating systems....Pages 91-91 Chaotic itineracy and clustered motion in globally coupled symplectic map system....Pages 93-99 Lyapunov analysis of stable chaos in self-gravitating many body systems....Pages 100-104 Stability of the modified Konishi-Kaneko system....Pages 105-110 Mixing transformations of N particles conserving almost all classical integrals....Pages 111-121 Symplectic integration without roundoff error....Pages 122-130 Discreteness noise versus force errors in N-body simulations....Pages 131-134 Core motions and global chaotic oscillations....Pages 135-150 N-body systems: Computer image and reality....Pages 151-157 The approach to integrability in N-body systems with a central point mass....Pages 158-162 On the non-trivial concept of relaxation in N-body systems....Pages 163-169 Gravothermal oscillations....Pages 170-176 Recent results on the stability of anisotropic stellar systems....Pages 177-180 The stability of the solar system....Pages 181-192 The one-dimensional three-body problem: Numerical simulations....Pages 193-198 Order and chaos in “collisionless” numerical simulations....Pages 199-216 On the permissible percentage of chaotic orbits in various morphological types of galaxies....Pages 217-225 Minimum energy states of a self-gravitating system....Pages 226-229 Effective collision term induced by coarse-graining....Pages 230-234 Theoretical and numerical investigation of the stability of flattened galaxies....Pages 235-238 The evolution of orbits in the stellar disk as a purely discontinuous random process....Pages 239-240 Interacting spherical stellar systems....Pages 241-256 How faithful are n-body simulations of disc galaxies? — artificial suppression of stellar dynamical instabilities....Pages 257-260 SPH simulations of the gas flow in normal spiral galaxies....Pages 261-263 Regular orbits and cantori in the potential of the barred galaxy NGC 936....Pages 264-266 The role of stochastic motion in a central field with a bar-like perturbation....Pages 267-267 A hierarchical model of patchy-structured galaxies and evolutionary processes....Pages 268-269 Evolution of clusters of galaxies....Pages 270-273 Smoothing of the cosmic background radiation by multiple gravitational scattering....Pages 274-277 Angular momentum of galaxies within the local supercluster....Pages 278-279 10 problems the solutions of which can seriously influence stellar dynamics....Pages 281-284 Comments on “10 key problems”....Pages 285-292 Explores the recent advances that have been made in research on the dynamics of stellar systems by applying the mathematical methods of ergodic theory and chaotic dynamics. The implications of current results and various aspects of the N-body problem are examined at length.