Periodic Solutions

  • Carl Ludwig Siegel
  • Jürgen K. Moser
Part of the Grundlehren der mathematischen Wissenschaften book series (CLASSICS, volume 187)


The theorem of Sundman discussed in chapter one represents the most far reaching result yet known about general solutions to the three- body problem. Unfortunately his ingenious method cannot be extended to the case n > 3. Although the results in § 6 can be used to exclude at the outset the simultaneous collision of all n bodies, the investigations of § 12, § 13 show that already a triple collision may give rise to essential singularities.


Periodic Solution Normal Form Power Series Hamiltonian System Equilibrium Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Carl Ludwig Siegel
    • 1
  • Jürgen K. Moser
    • 2
    • 3
  1. 1.Mathematisches InstitutUniversität GöttingenDeutschland
  2. 2.ETH Zentrum, MathematikZürichSchweiz
  3. 3.Courant Institute of Mathematical SciencesNew YorkUSA

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