Related papers: Henon's Isochrone Model
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
This paper illustrates the application of Lie transform normal-form theory to the construction of the 1:2 resonant normal form corresponding to a wide class of natural Hamiltonian systems. We show how to compute the bifurcations of the main…
We study the dynamics of spherically symmetric solutions in the Einstein Skyrme model. We focus our attention on generic long time evolution of initial data resulting in the formation of the B = 1 soliton, which plays the role of an…
The problem of constructing internally rotating solitons of fixed angular frequency $\omega$ in the Faddeev-Skyrme model is reformulated as a variational problem for an energy-like functional, called pseudoenergy, which depends…
In this paper, we study some interesting properties of a spherically symmetric oscillating soliton star made of a real time-dependent scalar field which is called an oscillaton. The known final configuration of an oscillaton consists of a…
This paper presents a study of the Poincar\'e-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant…
It is shown that the efficiency of the universe heating by an inflaton field depends not only on the possible presence of parametric resonance in the production of scalar particles but also strongly depends on the character of the inflaton…
We consider the three dimensional gravitational Vlasov Poisson system which is a canonical model in astrophysics to describe the dynamics of galactic clusters. A well known conjecture is the stability of spherical models which are…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of Universe and to solve the early universe pressing problems. For a resonable inflation model, the potential during inflation…
We analyze the ground states and the elementary collective excitations (phonons) of a class of systems, which form cluster crystals in the absence of attractions. Whereas the regime of moderate-to-high-temperatures in the phase diagram has…
We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the…
The H\'enon-Heiles system, initially introduced as a simplified model of galactic dynamics, has become a paradigmatic example in the study of nonlinear systems. Despite its simplicity, it exhibits remarkably rich dynamical behavior,…
The theory of isomorphs is reformulated by defining Roskilde-simple systems (those with isomorphs) by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a…
In classical field theory, radiation does not reflect off of reflectionless kinks. In quantum field theory, radiation quanta, called mesons, can be reflected. We provide a general analytical formula for the leading order amplitude and…
The conventional background solution for the evolution of a single canonical inflaton field performs admirably in extreme scenarios such as the slow-roll phase (where the slow-roll parameter is much less than one) and the deep reheating era…
We perform an extensive test of theoretical stellar models for main-sequence stars in ugriz, using cluster fiducial sequences obtained in the previous paper of this series. We generate a set of isochrones using the Yale Rotating…
In this paper, we study the Hamiltonian differential systems with homogeneous nonlinearity parts on $\mathbb{C}^2$. Firstly, we present a series of topological properties of polynomial Hamiltonian functions, with a particular focus on the…
Globular clusters rotate significantly, and with the increasing amount of detailed morphologicaland kinematical data obtained in recent years on galactic globular clusters many interesting features show up. We show how our theoretical…