Improbability of Collisions in $n$-Body Systems

Abstract

For a wide class of two-body interactions, including standard examples like gravitational or Coulomb fields, we show that collision orbits in $n$-body systems are of Liouville measure zero for all energies. We use techniques from symplectic geometry to relate the volume of the union of collision orbits to the area of Poincaré surfaces surrounding the collision set.

37 pages, 3 figures

References in corpus (1)

• Improbability of Wandering Orbits Passing Through a Sequence of Poincaré Surfaces of Decreasing Size

Cited by in corpus (2)

• Improbability of Wandering Orbits Passing Through a Sequence of Poincaré Surfaces of Decreasing Size
• Exponential stability of fast driven systems, with an application to celestial mechanics