Related papers: Orbit counting in polarized dynamical systems

We study the orbits and polynomial invariants of certain affine action of the super Weyl groupoid of Lie superalgebra $\mathfrak {gl}(n,m)$, depending on a parameter. We show that for generic values of the parameter all the orbits are…

We study the final architecture of planetary systems that evolve under the combined effects of planet-planet and planetesimal scattering. Using N-body simulations we investigate the dynamics of marginally unstable systems of gas and ice…

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…

We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.

We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…

We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.

We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…

We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…

Let $X$ be a finite set such that $|X|=n$, and let $k< n/2$. A group is $k$-homogeneous if it has only one orbit on the sets of size $k$. The aim of this paper is to prove some general results on permutation groups and then apply them to…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We define the orbit morphism of partial dynamical systems and prove that an orbit morphism being an isomorphism in the category of partial dynamical systems and orbit morphisms is equivalent to the existence of a continuous orbit…

We show the finiteness of perfect powers in orbits of polynomial dynamical systems over an algebraic number field. We also obtain similar results for perfect powers represented by ratios of consecutive elements in orbits. Assuming the…

For families of 4-regular directed circulant graphs with $n$ vertices, we count the number of primitive periodic orbits of length up to at least $n$. The relevant counting techniques are then extended to count the number of primitive pseudo…

This paper deals with some results concerning finitely generated coreduced comultiplication modules over a commutative ring.

Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X]^G in the case where G is reductive. Furthermore, we address the case where G is connected and…

We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible…

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to…

We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…

We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action…