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Improbability of Collisions in n-Body Systems

  • Stefan Fleischer
  • Andreas KnaufEmail author
Article
  • 14 Downloads

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.

Notes

Acknowledgements

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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