相关论文: Density of Orbits in Complex Dynamics

We give a negative answer to a question by J.M. Landsberg on the nature of normalizations of orbit closures. A counterexample originates from the study of complex, ternary, cubic forms.

We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…

A review article on the physics of beam-beam interactions in circular colliders.

In hyperbolic space density cannot be defined by a limit as we define it in Euclidean space. We describe the local density bounds for sphere packings and we discuss the different attempts to define optimal arrangements in hyperbolic space.

For a certain class of open quantum systems there exists a dynamical symmetry which connects different time-evolved density matrices. We show how to use this symmetry for dynamics in the Liouville space with time-dependent parameters. This…

Particles inside a planetary ring are subject to forcing due to the central planet, moons in inclined orbits, self-gravity of the ring and other forces due to radiation drag, collisional effects and Lorentz force due to magnetic field of…

In this paper I will approach the computation of the maximum density of regular lattices in large dimensions using a statistical mechanics approach. The starting point will be some theorems of Roger, which are virtually unknown in the…

We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…

Reply to a comment by T. Rakovszky, F. Pollmann, and C. W von Keyserlingk [arXiv:2010.07969].

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…

The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or…

It is shown that grey soliton dynamics in an one-dimensional trap can be treated as Landau dynamics of a quasi-particle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a…

In this work, we present a comprehensive and systematic study of the statistical complexity, originally introduced by L\'opez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209, 321-326 (1995)], across a broad range of compact star models. We…

We consider the dynamics of holomorphic polynomials in $\mathbb C$. We show that the ergodic properties of the map can be seen already from the real parts of the orbits.

We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.

We discuss various effective forms of Chebotarev's density theorem, answering a question of Serre and a question of Murty, Murty and Seradha.

The analysis of the spatial distribution and kinematics of galaxies in clusters allows one to determine the cluster internal dynamics. In this paper, I review the state of the art of this topic. In particular, I summarize what we have…

The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the…

We briefly review the foundations of a new relativistic fluid dynamics framework for polarized systems of particles with spin one half. Using this approach we numerically study the dynamics of the spin polarization of a rotating medium…

We use character sums to confirm several recent conjectures of V. I. Arnold on the uniformity of distribution properties of a certain dynamical system in a finite field. On the other hand, we show that some conjectures are wrong. We also…