Connecting planar linear chains in the spatial N-body problem

Planar Central Configuration Estimates in the N-body Problem

For all masses, there are at least n ?2 O 2-orbits of non-collinear planar central conngurations. In particular, this estimate is valid even if the potential function is not a Morse function. If the potential function is a Morse function, then an improved lower bound, on the order of n! ln ? n+1 3 =2, can be given.

Connecting orbits and invariant manifolds in the spatial restricted three-body problem

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-b...

Connecting Orbits and Invariant Manifolds in the Spatial Three-Body Problem

The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold tubes associated to libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body ...

The N-body Problem

On the Homology of the Integral Manifolds in the Planar N-body Problem

In the planar N-body problem, N point masses move in the plane under their mutual gravitational attraction. It is classical that the dynamics of this motion conserves the intgrals of motion: center of mass, linear momentum, angular momentum c, and energy h. Further, the motion has a rotational symmetry. The dynamics thus takes place on a (4N?7)-dimensional open manifold, known as the reduced in...