This article is cited in 10 papers

Special issue: In honor of Valery Kozlov for his 70th birthday

A Map for Systems with Resonant Trappings and Scatterings

Anton V. Artemyev^ab, Anatoly I. Neishtadt^bc, Alexei A. Vasiliev<sup>b

a</sup> Institute of Geophysics and Planetary Physics, University of California, Los Angeles, 90095, USA
^b Space Research Institute of RAS, ul. Profsoyuznaya 84/32, Moscow 117997, Russia
^c Loughborough University, Loughborough LE11 3TU, UK

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 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.

MSC: 37E40, 37M05

Received: 09.04.2019
Accepted: 04.12.2019

Language: English

DOI: 10.1134/S1560354720010025

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