Related papers: Standard map in magnetized relativistic systems: f…
The relative motion of material, point-like observers is analysed in terms of coordinate maps between the respective rest-frame of each observer. Under the assumption these maps are $C^{2}$-regular, conservation laws are deduced, which in…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an…
An exact solution of the Maxwell equations in Rindler coordinates is obtained. The electromagnetic field represents a wave preserving its shape in a relativistic uniformly accelerated frame. The relation with Airy beams is shown explicitly…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
The resonant interaction of relativistic electrons and whistler waves is an important mechanism of electron acceleration and scattering in the Earth radiation belts and other space plasma systems. For low amplitude waves, such an…
A novel imaging principle based on the interaction of electromagnetic waves with a beam of relativistic electrons is proposed. Wave-particle interaction is assumed to take place in a small spatial domain, so that each electron is only…
We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation,…
For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous…
Relativistic electromagnetic plasma waves are described by a dynamical equation that can be solved not only in terms of plane waves, but for several different accelerating wavepacket solutions. Depending on the spatial and temporal…
In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric…
A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
For the electromagnetic interaction of two particles the relativistic quantum mechanics equations are proposed. These equations are solved for the case when one particle has a small mass and moves freely. The initial wave functions are…
We consider a field theory describing interacting nonrelativistic particles of two types, which map to each other under time reversal, with point-like interaction. We identify a new type of interaction which depends on the relative velocity…
The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach…
Whereas nonrelativistic mechanics always connects the total momentum of a system to the motion of the center of mass, relativistic systems, such as interacting electromagnetic charges, can have internal linear momentum in the absence of…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
A neutral fixed point of a real iteration map $u$ becomes a super attracting fixed point using a suitable double newtonisation. The map $u$ is so transformed into a map $w$ which is here called the standard accelerator of $u$. The map $w$…