相关论文: Compactness and index of ordinary central configur…

Let $p$ be an odd prime number. We show that the modular isomorphism problem has a positive answer for finite $p$-groups whose center has index $p^3$, which is a strong contrast to the analogous situation for $p = 2$.

Planar central configurations can be seen as critical points of the reduced potential or solutions of a system of equations. By the homogeneity and invariance of the potential with respect to SO(2), it is possible to see that the…

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at…

In the Newtonian $n$-body problem for solutions with arbitrary energy, which start and end either at a total collision or a parabolic/hyperbolic infinity, we prove some basic results about their Morse and Maslov indices. Moreover for…

In this paper we show that in the $n$-body problem with harmonic potential one can find a continuum of central configurations for $n=3$. Moreover we show a counterexample to an interpretation of Jerry Marsden Generalized Saari's conjecture.…

We prove that, for generic (open and dense) values of the masses, the Newtonian potential function of the collinear N-body problem has $N!/2$ critical values when restricted to a fixed inertia level. In particular, we prove that for generic…

The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, -x, y, -y with x different from…

We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include…

For planar ($N$+1)-body ($N$\,$\geq$ 2) problem with a regular $N$-polygon, under the assumption that the ($N$+1)-th body locates at the geometric center of the regular $N$-polygon, we obtain the sufficient and necessary conditions that the…

This research investigates centered co-circular central configurations in the general power-law potential $n$-body problem. Firstly, there are no such configurations when all masses are equal, except for two; secondly, unless all masses are…

We provide a class of orbits in the curved N-body problem for which no point that could play the role of the centre of mass is fixed or moves uniformly along a geodesic. This proves that the equations of motion lack centre-of-mass and…

We prove for generalisations of quasi-homogeneous $n$-body problems with center of mass zero and $n$-body problems in spaces of negative constant Gaussian curvature that if the masses and rotation are fixed, there exists, for every order of…

The degeneracy of central configurations in the planar $N$-body problem makes their enumeration problem hard and the related dynamics appealing. To truly understand the bifurcations of central configurations, we should work in the FULL…

We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central configuration for each cyclic ordering of the masses.

We give a computer assisted proof of the full listing of central configuration for $n$-body problem for Newtonian potential on the plane for $n=5,6,7$ with equal masses. We show all these central configurations have a reflective symmetry…

We prove that if for the curved $n$-body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero.…

As an application of the representation theory for the dihedral groups, we study the symmetric central configurations in the n-body problem where $n$ equal masses are placed at the vertices of a regular $n$-gon. Since the Hessian matrices…

We study the problem of planar central configurations with $N$ heavy bodies and $k$ bodies with arbitrary small masses. We derive the equation which describe the limit of light masses going to zero, which can be seen as the equation for…

Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a…

The elliptic sine-Gordon equation in the plane has a family of explicit multiple-end solutions (soliton-like solutions). We show that all the finite Morse index solutions belong to this family. We also prove they are non-degenerate in the…