相关论文: The Determination of the Orbit Spaces of Compact C…

The P-matrix approach for the determination of the orbit spaces of compact linear groups enabled to determine all orbit spaces of compact coregular linear groups with up to 4 basic polynomial invariants and, more recently, all orbit spaces…

All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

We consider the problem of the determination of the isotropy classes of the orbit spaces of all the real linear groups, with three independent basic invariants satisfying only one independent relation. The results are obtained in the $\hat…

Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…

Invariant functions under the transformations of a compact linear group $G$ acting in $\real^n$ can be expressed in terms of functions defined in the orbit space of $G$. We develop a method to determine the isotropy classes of the orbit…

In many physical problems or applications one has to study functions that are invariant under the action of a symmetry group G and this is best done in the orbit space of G if one knows the equations and inequalities defining the orbit…

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…

Computational problems concerning the orbit of a point under the action of a matrix group occur throughout computer science, including in program analysis, complexity theory, quantum computation, and automata theory. In many cases the focus…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit…

The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on…

We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A…

A coregular space is a representation of an algebraic group for which the ring of polynomial invariants is free. In this paper, we show that the orbits of many coregular irreducible representations where the number of invariants is at least…

In this note we will consider reduction techniques for Hamiltonian systems that are invariant under the action of a compact Lie group $G$ acting by symplectic diffeomorphisms, and the related work on stability of relative equilibria. We…

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

The orbit polytope for a finite group G acting linearly and freely on a sphere S is used to construct a cellularized fundamental domain for the action. A resolution of the integers over G results from the associated G-equivariant…

We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…

The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct…