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.

中文翻译：

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具有共振陷波和散射的系统的映射

慢速动力学和共振现象可以在广泛的物理系统中找到，包括天体力学，流体力学和带电粒子动力学问题。在此类系统中，控制相空间中传输的重要共振效应是共振散射和陷获。对于具有弱扩散散射的系统，可以使用Chirikov标准图描述传输特性，并且图参数控制随机动力学和规则动力学之间的转换。在本文中，我们提出了具有强散射的共振系统的映射，该散射导致在相空间中发生非扩散性漂移，并在相空间中产生快速跳跃的陷阱。我们证明了此映射描述了随机动力学与常规动力学之间的过渡，并找到了此过渡的关键参数值。