相关论文: Point stabilisers for the enhanced and exotic nilp…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
We compute the fixed point index of non-degenerate central configurations for the $n$-body problem in the euclidean space of dimension $d$, relating it to the Morse index of the gravitational potential function $\bar U$ induced on the…
This is a sequel to \cite{osy} and \cite{sxy}. Associated with $G:=\GL_n$ and its rational representation $(\rho, M)$ over an algebraically closed filed $\bk$, we define an enhanced algebraic group $\uG:=G\ltimes_\rho M$ which is a product…
We prove that a nilpotent subgroup of orientation preserving $C^{1}$ diffeomorphisms of ${\mathbb S}^{2}$ has a finite orbit of cardinality at most two. We also prove that a finitely generated nilpotent subgroup of orientation preserving…
The generalized post-Keplerian parametrization for compact binaries on eccentric bound orbits is established at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories. This result is used to compute the…
We study the phase diagram of a twofold orbitally degenerate Anderson impurity model which presents a non-trivial fixed point similar to the two-impurity Kondo model one. Remarkably, this fixed point is more robust than the latter one,…
We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…
A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is…
In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii's theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
We consider an infinite-dimensional non-linear operator related to a hard core (HC) model with a countable set $\mathbb{N}$ of spin values. It is known that finding the fixed points of an infinite-dimensional operator is generally…
We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…
The $\mathrm{GL}(V)$-orbits in the enhanced nilpotent cone $V\times\mathcal{N}(V)$ are (essentially) in bijection with the orbits of a certain parabolic $P\subseteq\mathrm{GL}(V)$ (the mirabolic subgroup) in the nilpotent cone…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
We study the ring of regular functions of classical spherical orbits $R(\mathcal{O})$ for $G = Sp(2n,\mathbb{C})$. In particular, treating $G$ as a real Lie group with maximal compact subgroup $K$, we focus on a quantization model of…
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilibrium points, traveling waves, periodic orbits and invariant…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.
We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle…
A pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. [Astroph. J. 461 (1996) 565] is presented. This potential reproduces some of the general relativistic effects due to the spin angular momentum of the bodies,…