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On the integrability of the n-centre problem

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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.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, 91054, Erlangen, Germany

    Andreas Knauf

  2. Institute of Mathematics, 630090, Novosibirsk, Russia

    Iskander A. Taimanov

Authors
  1. Andreas Knauf
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  2. Iskander A. Taimanov
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Correspondence to Iskander A. Taimanov.

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Mathematics Subject Classification (2000): 70F10, 37J30, 37J35, 37N05, 70F15, 70H06, 81U10

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Knauf, A., Taimanov, I. On the integrability of the n-centre problem. Math. Ann. 331, 631–649 (2005). https://doi.org/10.1007/s00208-004-0598-y

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  • DOI: https://doi.org/10.1007/s00208-004-0598-y

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