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When circularly polarized wave scatters off a sphere, the scattered field forms a vortex with spiraling energy flow. This is due to the transformation of spin angular momentum into orbital one. Here we demonstrate that during this…
We consider surfaces with a double elliptic fibration, with two sections. We study the orbits under the induced translation automorphisms proving that, under natural conditions, the finite orbits are confined to a curve. This goes in a…
We consider the motion of electrons confined to a two dimensional plane with an externally applied perpendicular inhomogeneous magnetic field, both with and without a Coulomb potential. We find that as long as the magnetic field is…
We model a tidally forced star or giant planet as a Maclaurin spheroid, decomposing the motion into the normal modes found by Bryan (1889). We first describe the general prescription for this decomposition and the computation of the tidal…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
In a series of papers, we propose a theory to explain the formation and properties of rings and spirals in barred galaxies. The building blocks of these structures are orbits guided by the manifolds emanating from the unstable Lagrangian…
An study of the equatorial circular motion of photons and massive particles around a rotating compact body like a neutron star is presented. For this goal, we use an approximate Kerr-like metric with mass quadrupole as perturbation. 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…
We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to…
By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital…
It is proved that, according to Classical Mechanics and Electrodynamics, the trajectory of the center of mass of a neutral system of electrical charges can be deflected by an inhomogeneous magnetic field, even if its internal angular…
The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that the conjecture is true for orientation preserving…
Our previous study of a system of bodies assumed to move along almost circular orbits around a central mass, approximately described by Hill's equations, is extended to "exotic" [alias non-commutative] particles. For a certain critical…
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…
We study a class of maps having the Collatz function (famously related to the Collatz Conjecture) as an example, under the topological and ergodic perspectives, including an approach with thermodynamic formalism. By introducing a key…
A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have…
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
Let $X$ be a closed invariant subset of the half--open annulus $\mathbb{A}$ such that $\mathbb{A} \setminus X$ is homeomorphic to $\mathbb{A}$. We prove that either the rotation number of all forward semi--orbits of accessible points of $X$…
Studying Birkhoff sums of non-integrable functions involves the challenge of large observations depending on the sampled orbit, which prevents pointwise limit theorems. To address this issue, the largest observations are removed, this…