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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
Article

Abstract.

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.

Keywords

Entropy Positive Energy Celestial Mechanic Topological Entropy Independent Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

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

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