Related papers: On Orbit Spaces of Distributive Binary $G$-Spaces

The dynamics of a close binary system of globular clusters is considered. It is shown that the star transfer process from one of the components to the other should lead to the decrease of dimension of the first cluster with simultaneous…

Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a…

For a given small binary dihedral group G we use the classification of G-graphs to describe explicitly G-Hilb(C^2) by giving an affine open cover of M(Q,R), the moduli space of stable quiver representations.

This paper investigates the generation and properties of gravitational radiation within the framework of Generalized Brans-Dicke (GBD) theory, with a specific emphasis on its manifestation in compact binary systems. The primary focus of…

A widely considered characteristic of extra-solar planetary systems has been a seeming tendency for major axes of adjacent orbits to librate in stable configurations. Based on a new catalog of extra-solar planets (Butler et al. 2006) and…

Open orbits D of noncompact real forms G_0 acting on flag manifolds of their semisimple complexifications G are considered. The unique orbit C of a maximal compact subgroup K_0 of G_0 in D can be regarded as a point in the (full) cycle…

The effects which star cluster concentration and binarity have on observable parameters, that characterise the dynamical state of a population of stars after their birth aggregate dissolves, are investigated. To this end, the correlations…

The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are…

We present some preliminary results of our work about the close encounter of binary stars hosting planets on S-type orbits with the Sgr A* supermassive black hole in the center of our Galaxy.

Let $ \tilde{G} $ be an algebraic group acting on a variety $ \tilde{L} $, and $ G \subset \tilde{G} $ a subgroup which leaves a subvariety $ L \subset \tilde{L} $ stable. For a $ G $-orbit $ O_G = G u (u \in L) $ in $ L $, we can associate…

Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{k\"obaLOC25}, where one is based on the coorbit theory of Feichtinger-Gr\"ochening while the other is…

In this note I give a formula for calculating the number of orbits of irreducible binary forms of degree $n$ over GF$(p)$ under the action of GL$(2,p)$. This formula has applications to the classification of class two groups of exponent $p$…

Given a compact Lie group $G$, a reconstruction theorem for free $G$-manifolds is proved. As a by-product reconstruction results for locally trivial bundles are presented. Next, the main theorem is generalized to $G$-manifolds with one…

The statistical properties of planets in binaries were investigated. Any difference to planets orbiting single stars can shed light on the formation and evolution of planetary systems. As planets were found around components of binaries…

Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous…

Let $G$ be a real reductive Lie group and ${\tau}:G \longrightarrow GL(V)$ be a real reductive representation of $G$ with (restricted) moment map $m_{\ggo}: V-{0} \longrightarrow \ggo$. In this work, we introduce the notion of "nice space"…

We show that, if the family \cal{O} of orbits of all vector fields on a subcartesian space P is locally finite and each orbit in \cal{O} is locally closed, then \cal{O} defines a smooth Whitney A stratification of P. We also show that the…

We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existence of a type with bounded orbit. We prove almost exactness of…

Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of…

Wide binary stars are important for testing alternative models of gravitation in the weak-field regime and understanding the statistical outcomes of dynamical interactions in the general Galactic field. The Gaia mission's collection of…