Related papers: Unifying the Hyperbolic and Spherical 2-Body Probl…
Motivated by a model for the perception of textures by the visual cortex in primates, we analyse the bifurcation of periodic patterns for nonlinear equations describing the state of a system defined on the space of structure tensors, when…
In this paper, we prove the existence of super-hyperbolic orbits in four-body problem, which solves a conjecture of Marchal-Saari. We also prove the existence of noncollision singularities in the same model, which solves a conjecture of…
The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…
The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the…
Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three-dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of the…
The derivation scheme for hyperspherical harmonics (HSH) with arbitrary arguments is proposed. It is demonstrated that HSH can be presented as the product of HSH corresponding to spaces with lower dimensionality multiplied by the orthogonal…
In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central…
The different kinds of behaviour of three-body systems in the weak binding limit are classified with specific attention to the transition from a true three-body system to an effective two-body system. For weakly bound Borromean systems…
Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…
Negatively curved, or hyperbolic, regions of space in an FRW universe are a realistic possibility. These regions might occur in voids where there is no dark matter with only dark energy present. Hyperbolic space is strange and various…
In this work, based on consideration of periodicity and asymptotic forms of wave function, we propose a novel approach to the solution of finite volume three-body problem by mapping a three-body problem into a higher dimensional two-body…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.
We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei…
Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…
We identify as topological spheres those complete submanifolds lying with any codimension in hyperbolic space whose Ricci curvature satisfies a lower bound contingent solely upon the length of the mean curvature vector of the immersion.