Improbability of Collisions in n-Body Systems
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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.
We thank the anonymous reviewer for his/her helpful comments.
- 6.Saari, D.G.: Improbability of collisions in Newtonian gravitational systems. Trans. Amer. Math. Soc., 162, 267–271; erratum, ibid. 168(1972), 521, 1971Google Scholar