  Slow-fast dynamics and resonant phenomena can be found in a wide range of
physical systems, including problems of celestial mechanics, fluid mechanics,
and charged particle dynamics. Important resonant effects that control
transport in the phase space in such systems are resonant scatterings and
trappings. For systems with weak diffusive scatterings the transport properties
can be described with the Chirikov standard map, and the map parameters control
the transition between stochastic and regular dynamics. In this paper we put
forward the map for resonant systems with strong scatterings that result in
non-diffusive drift in the phase space, and trappings that produce fast jumps
in the phase space. We demonstrate that this map describes the transition
between stochastic and regular dynamics and find the critical parameter values
for this transition.
