Related papers: Orbits of charged particles with an azimuthal init…
We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our…
The motion of self-propelled particles can be rectified by asymmetric or ratchet-like periodic patterns in space. Here we show that a non-zero average drift can already be induced in a periodic potential with symmetric barriers when the…
This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of…
The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the…
We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\"oermer problem within a sphere, with the dipole in its centre. We start from a…
The Hamiltonian flow of the standard metric Hamiltonian with respect to the twisted symplectic structure on the cotangent bundle describes the motion of a charged particle on the base. We prove that under certain natural hypotheses the…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence…
The behavior of spinning particles in the stationary homogeneous magnetic field is considered and all types of trajectories for massive and massless particles are found. It is shown that spin of particles in a magnetic field is always…
The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In…
In this work, we study the motion of a magnetized particle orbiting a static and spherically symmetric black hole immersed in an external asymptotically uniform magnetic field in Einstein-dilaton-Gauss-Bonnet gravity. Similar to the…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
A model to study the dynamics of colloidal particles in nonuniform electric fields is proposed. For an isolated sphere, the conditions and threshold for sustained (Quincke) rotation in a linear direct current (dc) field are determined.…
The dipole-multipole transition in rapidly rotating dynamos is investigated through the analysis of forced magnetohydrodynamic waves in an unstably stratified fluid. The focus of this study is on the inertia-free limit applicable to…
In this paper we discuss epicycloid approximation of the trajectories of charged particles in axisymmetric magnetic fields. Epicycloid trajectories are natural in the Guiding Center approximation and we study in detail the errors arising in…
We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different…
The H\'{e}non-Heiles potential is undoubtedly one of the most simple, classical and characteristic Hamiltonian systems. The aim of this work is to reveal the influence of the value of the total orbital energy, which is the only parameter of…
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…
Periodic orbits (equivalence classes of closed paths up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra…