  There are many problems that lead to analysis of dynamical systems in which
one can distinguish motions of two types: slow one and fast one. An averaging
over fast motion is used for approximate description of the slow motion. First
integrals of the averaged system are approximate first integrals of the exact
system, i.e. adiabatic invariants. Resonant phenomena in fast motion (capture
into resonance, scattering on resonance) lead to inapplicability of averaging,
destruction of adiabatic invariance, dynamical chaos and transport in large
domains in the phase space. In the paper perturbation theory methods for
description of these phenomena are outlined. We also consider as an example the
problem of surfatron acceleration of a relativistic charged particle.
