Applying closed-orbit theory to the recurrence spectra of the hydrogen atom in a magnetic field, one can interpret most, but not all, structures semiclassically in terms of closed classical orbits. In particular, conventional closed-orbit theory fails near bifurcations of orbits where semiclassical amplitudes exhibit unphysical divergences. Here we analyze the role of ghost orbits living in com...

This paper investigates the design of the relative motion orbits of geostationary satellites in the presence of geometric constraints. A geometric constraint is defined by a sensor’s pointing direction and field of view. An analyis was made of the underlying geometry of the relative orbits associated to geometric constraints. This resulted in the derivation of novel relations between relative o...

Gutzwiller's trace formula for the semiclassical density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation (" ghost orbits ") can produce pronounced signatures in the semiclassical spectra in the vi...

We present cuspy, non–axisymmetric, scale–free mass models of discs, whose gravitational potentials are of Stäckel form in parabolic coordinates. A black hole may be added at the centre, without in any way affecting the Stäckel form; the dynamics in these potentials is, of course, fully integrable. The surface density, Σdisc ∝ 1/r γ , where 0 < γ < 1 corresponds to steep cusps for which the cen...

A new algorithm for extracting de Haas – van Alphen frequencies, effective masses, and electronic density of states contributions from calculated band energies is presented. The algorithm creates an interpolated k-space " super cell " , which is broken into slices perpendicular to the desired magnetic field direction. Fermi surface orbits are located within each slice, and de Haas – van Alphen ...

The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years there has been rapid progress in the development of a bifurcation theory for symmetric dynamical systems. But there are hardly any results on the numerical computation of those bifurcations yet. In this paper we show how spatiotemporal symmetries of periodic orbits can be e...

This paper concerns homoclinic solutions to periodic orbits in a fourth-order Hamiltonian system arising from a reduction of the classical water-wave problem in the presence of surface tension. These solutions correspond to travelling solitary waves which converge to non-decaying ripples at innnity. An analytical result of Amick and Toland, showing the existence of such homoclinic orbits to sma...

PURPOSE To evaluate the surgical outcome of deep lateral orbital decompression with or without rim removal. DESIGN Retrospective case series. METHODS Thirty-two patients (47 orbits) with Graves' orbitopathy who underwent simple deep lateral decompression or balanced lateral plus medial decompression. Of the 14 patients (24 orbits) who underwent simple deep lateral decompression, 8 (13 orbit...

The theory of chaotic dynamical systems gives many tools that can be used in climate studies. The widely used ones are the Lyapunov exponents, the Kolmogorov entropy and the attractor dimension characterizing global quantities of a system. Another potentially useful tool from dynamical system theory arises from the fact that the local analysis of a system probability distribution function (PDF)...