Related papers: Less trouble with orbits: The semi-classical hydro…
We present a new extensive analysis of the old problem of finding a satisfactory calibration of the relation between the geometric albedo and some measurable polarization properties of the asteroids. To achieve our goals, we use all…
We study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of four-dimensional systems which may be Hamiltonian or not. Only one parameter is enough to treat these types of bifurcations in Hamiltonian systems but…
In this paper, we investigate so-called spherical photon orbits around a deformed Kerr black hole with an extra deformation parameter. The change in the azimuth $\Delta\varphi$ and the angle of dragging of nodes per revolution $\Delta\Omega…
A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…
A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for…
We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (\rho,z,p_\rho,p_z) and have p_\phi = m\hbar where m is the azimuthal…
Garsia and Procesi, in their study of Springer's representation, proved that the cohomology ring of a Springer fiber is isomorphic to the associated graded ring of the coordinate ring of the $S_n$ orbit of a single point in $\mathbb{C}^n$.…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is,…
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Two satellites with mean orbital elements which differ only in terms of right ascension of the ascending node, argument of perigee, and mean anomaly are notable for having the same mean orbital element secular drift rates due to the J2…
Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are…
The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A…
A higher order theory of gravitation is considered which is obtained by modifying Einstein field equations. The Lagrange used to modify this in the form a polynomial in (scalar curvature) R. In this equation we have studied spherical…
In the paper, only Static Spherically Symmetric space-times in four dimensions are considered within modified gravity models. The non-singular static metrics, including black holes not admitting a de Sitter core in the center and…
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same…
Recurrence relations of perturbation theory for hydrogen ground state are obtained. With their aid polarizabilities in constant perpendicular electric and magnetic fields are computed up to 80th order. The high orders asymptotic is compared…
Account of an intrinsic spin-orbit coupling in the valence bands of common semiconductors yields the scalar spin-orbit-rotation term in the effective-mass Hamiltonian of the conduction-band electron. This result is obtained within the…
Hamiltonian normal forms allow for the analytical approximation of center manifold trajectories and their invariant manifolds through the separation of the saddle and center subspaces that make up the dynamics at the collinear libration…