Hyperbolic relative equilibria for the negative curved n–body problem

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Stability of Relative Equilibria in the Planar n-Vortex Problem

We study the linear and nonlinear stability of relative equilibria in the planar n-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological approach is taken to show that for the case of positive circulations, a relative equilibrium is linearly stable if and only if it is a nondegenerate minimum...

Finiteness of Relative Equilibria of the Four-body Problem

We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.

On polygonal relative equilibria in the N-vortex problem

Helmholtz’s equations provide the motion of a system of N vortices which describes a planar incompressible fluid. A relative equilibrium is a particular solution of these equations for which the distances between the particles are invariant during the motion. In this article, we are interested in relative equilibria formed of concentric regular polygons of vortices. We show that in the case of ...

Central configurations and relative equilibria in the n–body problem