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.- Some clues about the dynamics of globular clusters from high-resolution observation.- Diffusion of stellar orbits in the galactic disk.- Ergodic methods in stellar dynamics.- On a notion of weak stability and its relevance for celestial mechanics and molecular dynamics.- Recent developments in the dynamics of nonlinear Hamiltonian systems with many degrees of freedom.- Numerical exploration of the circular billiard with gravity.- Ergodicity and mixing in gravitating systems.- Chaotic itineracy and clustered motion in globally coupled symplectic map system.- Lyapunov analysis of stable chaos in self-gravitating many body systems.- Stability of the modified Konishi-Kaneko system.- Mixing transformations of N particles conserving almost all classical integrals.- Symplectic integration without roundoff error.- Discreteness noise versus force errors in N-body simulations.- Core motions and global chaotic oscillations.- N-body systems: Computer image and reality.- The approach to integrability in N-body systems with a central point mass.- On the non-trivial concept of relaxation in N-body systems.- Gravothermal oscillations.- Recent results on the stability of anisotropic stellar systems.- The stability of the solar system.- The one-dimensional three-body problem: Numerical simulations.- Order and chaos in collisionless numerical simulations.- On the permissible percentage of chaotic orbits in various morphological types of galaxies.- Minimum energy states of a self-gravitating system.- Effective collision term induced by coarse-graining.- Theoretical and numerical investigation of the stability of flattened galaxies.- The evolution of orbits in the stellar disk as a purely discontinuous random process.- Interacting spherical stellar systems.- How faithful are n-body simulations of disc galaxies? artificial suppression of stellar dynamical instabilities.- SPH simulations of the gas flow in normal spiral galaxies.- Regular orbits and cantori in the potential of the barred galaxy NGC 936.- The role of stochastic motion in a central field with a bar-like perturbation.- A hierarchical model of patchy-structured galaxies and evolutionary processes.- Evolution of clusters of galaxies.- Smoothing of the cosmic background radiation by multiple gravitational scattering.- Angular momentum of galaxies within the local supercluster.- 10 problems the solutions of which can seriously influence stellar dynamics.- Comments on 10 key problems.