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Slow-fast dynamics and resonant phenomena can be found in a wide range ofphysical systems, including problems of celestial mechanics, fluid mechanics,and charged particle dynamics. Important resonant effects that controltransport in the phase space in such systems are resonant scatterings andtrappings. For systems with weak diffusive scatterings the transport propertiescan be described with the Chirikov standard map, and the map parameters controlthe transition between stochastic and regular dynamics. In this paper we putforward the map for resonant systems with strong scatterings that result innon-diffusive drift in the phase space, and trappings that produce fast jumpsin the phase space. We demonstrate that this map describes the transitionbetween stochastic and regular dynamics and find the critical parameter valuesfor this transition.

A map for systems with resonant trappings and scatterings