For the three body problem with equal masses, we prove that the most symmetric
continuation class of Lagrange's equilateral triangle solution, also referred to as the $ P …

For a nondegenerate analytic system with a conserved quantity, a classic result by
Lyapunov guarantees the existence of an analytic manifold of periodic orbits tangent to any …

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 …

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 …

The paper investigates a generalization of the classical Sitnikov problem, concentrating on
the movement of a satellite along the Z-axis as it interacts with $ n $ primary bodies in …

We prove the existence of periodic solutions of the N=(n+ 1)-body problem starting with n
bodies whose reduced motion is close to a non-degenerate central configuration and …

The time-dependent restricted (n+ 1)(n+ 1)-body problem concerns the study of a massless
body (satellite) under the influence of the gravitational field generated by n primary bodies …

We study periodic solutions of the discrete nonlinear Schrödinger equation (DNLSE) that
bifurcate from a symmetric polygonal relative equilibrium containing n sites. With specialized …

Hip-hop solutions of the-body problem are solutions that satisfy, at every instance of time,
that the bodies with the same mass are at the vertices of two regular-gons, and each one of …