Stochastic Motion of Relativistic Particles in the Field of a Wide Wave Packet

Stochastic motion of relativistic particles in the field of a wave packet propagating under an angle to the external magnetic field are investigated. The interplay of the dynamical and statistical aspects of the behavior of the relativistic particle-potential wave packet system is considered. Dynamics of this system are described by nonlinear mapping and corresponding Fokker-Planck-Kolmogorov equation in phase space possesses canonical Hamiltonian structure. The following general problems of stochastic motion are disscussed: local instability and the Lyapunov exponents and the Kolmogorov entropy; a fractal structures and its dimension; bifurcations of a vector fields and the boundaries of the region of dynamical chaos. The results of numerical simulation are presented. A possible astrophysical application of the results obtained is discussed