Related papers: Density of Orbits in Complex Dynamics
Orbital dynamics in time-reversal-symmetric centrosymmetric systems is examined theoretically. Contrary to common belief, we demonstrate that many aspects of orbital dynamics are qualitatively different from spin dynamics because the…
Maxwell's investigations into the stability of Saturn's rings provide one of the earliest analyses of the dynamics of astrophysical discs. Current research in planetary rings extends Maxwell's kinetic theory to treat dense granular gases of…
This is an expository article on relating the Chebotarev Density Theorem to the Bateman-Horn constant.
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…
An equation previously proposed to describe the evolution of vortex line density in rotating counterflow turbulent tangles in superfluid helium is generalized to incorporate nonvanishing barycentric velocity and velocity gradients. Our…
The generalization of Bertrand's theorem to the case of the motion of point particle on the surface of a cone is presented. The superintegrability of such models is discussed. The additional integrals of motion are analyzed for the case of…
This exploration of solutions for the orbits of Local Group galaxies under the cosmological initial condition of growing peculiar velocities and fitted to measured distances, redshifts, and proper motions reveals a considerable variety of…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
The intrinsic volumes are measures of the content of a convex body. This paper uses probabilistic and information-theoretic methods to study the sequence of intrinsic volumes of a convex body. The main result states that the intrinsic…
The aim of the present paper is to provide suficient conditions for the existence of periodic solutions of the perturbed attitude dynamics of a rigid dumbbell satellite in a circular orbit.
This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion,…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
We present and validate a novel semi-analytical approach to study the effect of dynamical friction on the orbits of massive perturbers in rotating stellar discs. We find that dynamical friction efficiently circularises the orbit of…
We describe results on the dynamics of polynomial diffeomorphisms of ${\bf C^2}$ and draw connections with the dynamics of polynomial maps of ${\bf C}$ and the dynamics of polynomial diffeomorphisms of ${\bf R^2}$ such as the H\'enon…
We are interested in finding a dense part of the space of $C^1$-diffeomorphisms which decomposes into open subsets corresponding to different dynamical behaviors: we discuss results and questions in this direction. In particular we present…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
Selected problems in heavy quark physics are discussed. The wealth of research problems in this field of physics is stressed.
This paper addresses resonantly forced spiral density waves in a dense planetary ring which is close to the threshold for viscous overstability. We solve numerically the hydrodynamical equations for a dense, axisymmetric thin disk in the…