Anton Artemyev
Publications:
Artemyev A. V., Neishtadt A. I., Vasiliev A. A.
A Map for Systems with Resonant Trappings and Scatterings
2020, vol. 25, no. 1, pp. 210
Abstract
Slowfast 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.

Neishtadt A. I., Vasiliev A. A., Artemyev A. V.
Capture into Resonance and Escape from it in a Forced Nonlinear Pendulum
2013, vol. 18, no. 6, pp. 686696
Abstract
We study the dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the unperturbed pendulumâ€™s oscillations, the pendulum can be captured into resonance. The captured pendulum oscillates in such a way that the resonance is preserved, and the amplitude of the oscillations accordingly grows. We consider this problem in the frames of a standard Hamiltonian approach to resonant phenomena in slowfast Hamiltonian systems developed earlier, and evaluate the probability of capture into resonance. If the system passes through resonance at small enough initial amplitudes of the pendulum, the capture occurs with necessity (socalled autoresonance). In general, the probability of capture varies between one and zero, depending on the initial amplitude. We demonstrate that a pendulum captured at small values of its amplitude escapes from resonance in the domain of oscillations close to the separatrix of the pendulum, and evaluate the amplitude of the oscillations at the escape.

Neishtadt A. I., Artemyev A. V., Zelenyi L. M.
Regular and chaotic charged particle dynamics in low frequency waves and role of separatrix crossings
2010, vol. 15, nos. 45, pp. 564574
Abstract
We consider interaction of charged particles with an electromagnetic (electrostatic) low frequency wave propagating perpendicular to a uniform background magnetic field. The effects of particle trapping by the wave and further acceleration of a surfatron type are discussed in details. Method for this analysis based on the adiabatic theory of separatrix crossing is used. It is shown that particle can unlimitedly accelerate in the trapping in electromagnetic waves and energy of particle does not increase for the system with electrostatic wave.
