We consider the equations of motion of n vortices of equal circulation in the plane, in a disk
and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference …

We develop a systematic approach for proving the existence of choreographic solutions in
the gravitational n body problem. Our main focus is on spatial torus knots: that is, periodic …

Given n point masses turning in a plane at a constant speed, this paper deals with the global
bifurcation of periodic solutions for the masses in that plane and in space. As a special case …

The existence of periodic solutions in Γ-symmetric Newtonian systems x¨=−∇ f (x) can be
effectively studied by means of the Γ× O (2)-equivariant gradient degree with values in the …

This paper gives an analysis of the movement of n+ 1 almost parallel filaments or vortices.
Starting from a polygonal equilibrium of n vortices with equal circulation and one vortex at …

We use numerical continuation and bifurcation techniques in a boundary value setting to
follow Lyapunov families of periodic orbits and subsequently bifurcating families. The …

A model derived in (Klein et al., J Fluid Mech 288: 201–248, 1995) for n near-parallel vortex
filaments in a three dimensional fluid region takes into consideration the pairwise interaction …

This paper gives an analysis of the movement of n vortices on the sphere. When the vortices
have equal circulation, there is a polygonal solution that rotates uniformly around its center …

We consider the N-vortex problem on the sphere assuming that all vortices have equal
strength. We develop a theoretical framework to analyse solutions of the equations of motion …

We study equations for the mechanical movement of chains of identical particles in the plane
interacting with their nearest-neighbors by bond stretching and by van der Waals and …