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 nondiffusive 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.
Keywords:
scattering on resonance, capture into resonance
Citation:
Artemyev A. V., Neishtadt A. I., Vasiliev A. A., A Map for Systems with Resonant Trappings and Scatterings, Regular and Chaotic Dynamics,
2020, Volume 25, Number 1,
pp. 2-10