On the integrability of the n-centre problem

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• 作者：Andreas Knauf and Iskander A. Taimanov
• 刊名：Mathematische Annalen
• 出版年：2005
• 出版时间：March 2005
• 年：2005
• 卷：331
• 期：3
• 页码：631-649
• 全文大小：202 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

It is known that for n3 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.