This book addresses a broad range of problems related to observed manifestations of chaotic motions in galactic and stellar objects, by invoking basic theory, numerical modeling, and observational evidence. For the first time, methods of stochastic dynamics are applied to actually observed astronomical objects, e.g. the gaseous disc of the spiral galaxy NGC 3631. In the latter case, the existence of chaotic trajectories in the boundary of giant vortices was recently found by the calculation of the Lyapunov characteristic number of these trajectories.

The reader will find research results on the peculiarities of chaotic system behaviour; a study of the integrals of motion in self-consistent systems; numerical modeling results of the evolution process of disk systems involving resonance excitation of the density waves in spiral galaxies; a review of specific formations in stars and high-energy sources demonstrating their stochastic nature; a discussion of the peculiarities of the precessional motion of the accretion disk and relativistic jets in the double system SS 433; etc.

This book stands out as the first one that deals with the problem of chaos in real astrophysical objects. It is intended for graduate and post-graduate students in the fields of non-linear dynamics, astrophysics, planetary and space physics; specifically for those dealing with computer modeling of the relevant processes.

On August 2000 in the Lomonosov Moscow State University the first scientific conference dedicated to chaos in the real astronomical systems was held. The most prominent astrophysisists - specialist in the field of stochastic dynamics - attended the conference. A broad scope of the problems related to the observed manifes tations of chaotic motions in galactic and stellar objects, with the involvement of basic theory and numerical modeling, were addressed. The idea (not so obvious, as we believe, to many astrophysicists) was to show that, while great progress in the field of stochastic mechanics was accomplished, the science of chaos in actually observed systems is only just being born. Basically, the situation described prompted the organizers to hold the meeting in order to discuss chaotic processes in real systems. It seemed worthwhile to begin these introductory remarks with a brief descrip tion of some events that preceeded the conference. Since actually existing systems are the subject of the natural sciences, and in the latter experiments play the key role, we shall begin our account with the experimental results."