The Schwarzschild potential, defined as U (r)=-A/rB/r^ 3 U (r)=-A/rB/r 3, where rr is the
relative distance between two mass points and A, B> 0 A, B> 0, models astrophysical and …

We consider a generalization of the famous Lennard-Jones potential. To study the two-body
problem associated to this potential, we use the foliations of the phase space by the …

We consider the planar restricted (N+ 1)-body problem where the interaction potential
between the particle and the primaries is taken to be a finite sum of terms of the form …

Abstract The planar symmetrical (n+ 1)-body problem in a Manev-type field (featured by a
potential of the form α/r+ β/r 2) is being tackled. One proves that, if n equal masses are …

The null geodesics of a Schwarzschild black hole are studied from a dynamical system's
perspective. Written in terms of Kerr–Schild coordinates, the null geodesic equation takes on …

A relative equilibrium is a periodic orbit of the n-body problem that rotates uniformly
maintaining the same central configuration for all time. In this paper we generalize some …

In this dissertation we analyse from a qualitative standpoint motion in a quasihomogeneous
potential field: we offer a complete description of the flow associated with the two-body …

Abstract We consider the (1+ 4)-body problem with a Newtonian potential augmented by a “J
2” inverse-cubic perturbation. We describe the square-shaped homographic motions, and …

The Poincaré compactification is an extension of a polynomial vector field to a compact
manifold. We generalize this construction to quasihomogeneous vector fields which are …

Using the techniques of equivariant bifurcation theory we prove the existence of non-
stationary periodic solutions of Γ-symmetric systems q¨(t)=−∇ U (q (t)) in any neighborhood …