Archive for Rational Mechanics and Analysis

, Volume 234, Issue 3, pp 1007–1039 | Cite as

Improbability of Collisions in n-Body Systems

  • Stefan Fleischer
  • Andreas KnaufEmail author


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.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsFriedrich-Alexander-University Erlangen-NürnbergErlangenGermany

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