Related papers: Epicycles in hyperbolic sky
R-mode oscillations in a rotating star produce characteristic signatures in a Fourier amplitude spectrum at frequencies related with the rotation frequency, which can be, in turn, used to obtain the surface rotation rate of the star. Some…
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun")…
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in…
This paper builds two detailed examples of generalized normal in non-Euclidean spaces, i.e. the hyperbolic and elliptic geometries. In the hyperbolic plane we define a n-sided hyperbolic polygon P, which is the Euclidean closure of the…
The paper concerns the problem for the ultrahyperbolic equation in the Euclidean space with data on a characteristic hyperplane. Smoothness and asymptotics of the solution along characteristic lines transversal to the initial hyperplane are…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a…
We describe the structure and composition of six major stellar streams in a population of 20 574 local stars in the New Hipparcos Reduction with known radial velocities. We find that, once fast moving stars are excluded, almost all stars…
Let us consider a reference frame Sigma prime in which the pseudo-Euclidean geometry holds. Einstein assumed that the principle of special relativity is valid, i.e. the reference frame of any uniformly moving observer is also described by…
We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces, and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of…
We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch the vacuum with finite radii, and the linearized equation around one of the equilibria has…
A two-layer spherical $\alpha^2$-dynamo model consisting of an inner electrically conducting core (magnetic diffusivity $\lambda_i$ and radius $r_i$) with $\alpha = 0$ surrounded by an electrically conducting spherical shell (magnetic…
We present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincar\'e disc D. Different types of patterns are…
The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal…
In this talk we shall show a perfect fluid cosmological model and its properties. The model possesses an orthogonally transitive abelian two-dimensional group of isometries that corresponds to cylindrical symmetry. The matter content is a…
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is the hyperbolic plane we proved in [13] the existence and…
Spiral arms are observed in numerous protoplanetary discs. These spiral arms can be excited by companions, either on bound or unbound orbits. We simulate a scenario where an unbound perturber, i.e. a flyby, excites spiral arms during a…
The Milky Way is a spiral galaxy with the Schechter characteristic luminosity $L_*$, thus an important anchor point of the Hubble sequence of all spiral galaxies. Yet the true appearance of the Milky Way has remained elusive for centuries.…
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…
In this paper we review some author's results about Weingarten surfaces in Euclidean space $\r^3$ and hyperbolic space $\h^3$. We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property.…