Mathematische Annalen

, Volume 331, Issue 3, pp 631–649 | Cite as

On the integrability of the n-centre problem

  • Andreas Knauf
  • Iskander A. TaimanovEmail author


It is known that for n≥3 centres and positive energies the n-centre problem of celestial mechanics leads to a flow with a strange repellor and positive topological entropy. Here we consider the energies above some threshold and show: Whereas for arbitrary g>1 independent integrals of Gevrey class g exist, no real-analytic (that is, Gevrey class 1) independent integral exists.


Entropy Positive Energy Celestial Mechanic Topological Entropy Independent Integral 
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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Institute of MathematicsNovosibirskRussia

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