Related papers: Narrow rings: a scattering billiard model
We study the final architecture of planetary systems that evolve under the combined effects of planet-planet and planetesimal scattering. Using N-body simulations we investigate the dynamics of marginally unstable systems of gas and ice…
Accretion onto black holes in wind-fed binaries and in collapsars forms small rotating discs with peculiar properties. Such ``mini-discs'' accrete on the free-fall time without help of viscosity and nevertheless can have a high radiative…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
We discuss quantum dynamics in the ring systems with double Y-junctions in which two arms have same length. The node of a Y-junction can be parametrized by U(3). Considering mathematically permitted junction conditions seriously, we…
For typical cocycles over subshifts of finite type, we show that for any given orbit segment, we can construct a periodic orbit such that it shadows the given orbit segment and that the product of the cocycle along its orbit is a proximal…
In two-dimensional space, we investigate the slow dynamics of multiple localized spots with oscillatory tails in a specific three-component reaction-diffusion system, whose key feature is that the spots attract or repel each other…
Most planetary systems are formed within stellar clusters, and these environments can shape their properties. This paper considers scattering encounters between solar systems and passing cluster members, and calculates the corresponding…
We investigate flat maps where the source or target is a Noetherian ring, giving necessary and/or sufficient conditions on a ring for such maps to exist. Along the way, we develop some general facts about flat ring maps, and exhibit many…
We present a scenario for the production of dynamically cold rings around the Milky Way via a high-eccentricity, flyby encounter. These initial conditions are more cosmologically motivated than those considered in previous works. We find…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
The discovery that many trans-neptunian objects exist in pairs, or binaries, is proving invaluable for shedding light on the formation, evolution and structure of the outer Solar system. Based on recent systematic searches it has been…
Based on the secular theory, we discuss the orbital evolution of stars in a nuclear star cluster to which a secondary massive black hole is infalling with vanishing eccentricity. We find that the eccentricities of the stars could show sharp…
Sequences of infinitesimally thin, uniformly rotating, self-gravitating relativistic discs with internal two-dimensional pressure have been constructed. It is shown that in weaker relativistic configurations the sequences undergo a…
We study the effect of edge diffraction on the semiclassical analysis of two dimensional quantum systems by deriving a trace formula which incorporates paths hitting any number of vertices embedded in an arbitrary potential. This formula is…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
Several stars show deep transits consistent with discs of roughly 1 Solar radius seen at moderate inclinations, likely surrounding planets on eccentric orbits. We show that this configuration arises naturally as a result of planet-planet…
We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
Planetary rings are not only ubiquitous around the giant planets in the outer Solar System, but have also been discovered around several small distant bodies. In contrast, no rings have been observed around any inner Solar System objects.…