Chaos in dissipative relativistic standard maps

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

“…Based on the well known dissipative standard map [1] the authors of Ref. [5] introduced a dissipative relativistic standard map (DRSM), that is a discrete time system described as a transformation onto the real plane to itself f (x, y) : R 2 → R 2 , used to investigate the dynamics of a massive charged particle in the electric field of an electromagnetic wave packet. The main aim was describe how relativistic effects change the nonlinear dynamics presented by a dissipative standard map.…”

“…In the present work we revisit the investigation of nonlinear dynamics of a particle described by a dissipative relativistic standard map (DRSM), introduced by [5] and later explored in [7,8,9] and, specially extend the study published by Oliveira and Leonel in the Ref. [10], where the authors investigated the statistical and dynamical behaviors for conservative and dissipative relativistic particles in waveguide.…”

“…A well know discrete time system or map used to describe the dynamics of a relativistic particle in a wave packet was originally proposed in Ref. [2], revisited in [3,4] and extended to dissipative regime in [5]. A natural question arises from this scenario when one intends to submit a dissipative relativistic particle to thermal effects modeled by Gaussian noise added to the system: what are the most common effects caused by noise in the periodic underlying dynamics of charged particles as function of temperature of thermal environment?…”

Statistical Predictions for the Dynamics of a Low-Speed System: Newtonian versus Special-Relativistic Mechanics

“…Since βP<<1 implies v<<c (i.e., low speed), where v is the particle speed and c is the speed of light. Ciubotariu et al [13] have studied a dissipative version of the relativistic standard map to see how weak damping changes the phase-space structure around the origin described by the relativistic standard map; they did not however compare the dynamical predictions of their dissipative relativistic standard map with the predictions of the dissipative non-relativistic standard map.…”

Constant-Phase-Induced Control of Chaotic Charged Particles in the Field of a Wave Packet

“…As is well known, the structure of the wave packet reflects the particular physical situation that is being considered in each case. In this regard, a canonical, widely studied particular case is that of an infinite set of waves having the same amplitudes and wave numbers, zero constant phases, and integer frequencies [Chirikov, 1979;Wenzel et al, 1991;Chernikov et al, 1989;Nomura et al, 1992;Ciubotariu et al, 2002]. While the Hamiltonian approach to the general problem is suitable in many physical contexts [Mackay & Meiss, 1987], the consideration of dissipative forces seems appropriate so as to take into account such diverse phenomena as electron-ion collisions, energy losses through synchrotron radiation, and stochastic heating of particles in plasma physics.…”