# A map for systems with resonant trappings and scatterings

## TL;DR

This paper introduces a new map model for resonant systems with strong scatterings and trappings, capturing the transition between stochastic and regular dynamics in phase space.

## Contribution

It develops a novel map for systems with strong scatterings and trappings, extending previous models to describe non-diffusive drift and fast jumps in phase space.

## Key findings

- The map describes the transition between stochastic and regular dynamics.
- Critical parameter values for phase space transition are identified.
- The model applies to a wide range of physical systems with resonant phenomena.

## Abstract

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.