Related papers: Numerical Study of Polytropes with n=1 and Differe…

For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration…

A new type of long-lived solitary structures for paraxial optics with two circular polarizations of light in a homogeneous defocusing Kerr medium with an anomalous group velocity dispersion has been revealed numerically in the coupled…

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type $\bold{E}_6$ singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of which…

We analytically construct an infinite number of trapped toroids in spherically symmetric Cauchy hypersurfaces of the Einstein equations. We focus on initial data which represent "constant density stars" momentarily at rest. There exists an…

We analyze planar $n$-body Hamiltonian systems with quadratic $D_n$-invariant interactions and identify the symmetry obstruction to choreographic motion. Choreographies are taken throughout to be collision-free solutions of the equations of…

This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…

We study a possibility of existence of localized two-dimensional structures, both smooth and non-smooth, that can move without significant change of their shape in a leading stream of compressible barotropic fluid on a rotating plane.

We study the evolution of the phase-space of collisionless N-body systems under repeated stirrings or perturbations. We find convergence towards a limited solution group, in accordance with Hansen 2010, that is independent of the initial…

We start with a variational approach and derive a set of coupled integral equations for the bound states of $N$ identical spin-$\uparrow$ fermions and a single spin-$\downarrow$ fermion in a generic multiband Hubbard Hamiltonian with an…

A polytope $P$ is circumscribed about a convex body $\Phi\subset \mathbb{R}^n$ if $\Phi\subset P$ and each facet of $P$ is contained in a support hyperplane of $\Phi$. We say that a convex body $\Phi\subset \mathbb{R}^n$ is a rotor of a…

We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of…

We investigate the superintegrability of rigid body rotors coupled to planar systems. In particular, we study the isotropic harmonic oscillator in two dimensions, with its (central) force acting on the rotor's center of mass constrained to…

Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space P^n and let \Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following [1], we show that…

We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping…

An $(n+1)$-toroid is a quotient of a tessellation of the $n$-dimensional Euclidean space with a lattice group. Toroids are generalizations of maps in the torus on higher dimensions and also provide examples of abstract polytopes. Equivelar…

We study the asymptotic behavior of the cardinality of the fixed point set of iterates of an endomorphism of a complex torus. We show that there are precisely three types of behavior of this function: it is either an exponentially growing…

We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conjecture this to be true for an arbitrary number of ramification…

Anisotropy is important for the existence of true long range order in two dimensional (2D) systems. This is firmly exemplified by the $q$-state clock models in which discreteness drives the quasi-long range order into a true long range…

We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon.

The energy minimization problem associated to uniform, isotropic, linearly elastic rods leads to a geometric variational problem for the rod centerline, whose solutions include closed, knotted curves. We give a complete description of the…