On the integrability of the n-centre problem

Knauf A, Taimanov IA (2005)

Publication Type: Journal article

Publication year: 2005

Journal

Mathematische Annalen Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 331

Pages Range: 631--649

Journal Issue: 3

DOI: 10.1007/s00208-004-0598-y

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.

Authors with CRIS profile

Andreas Knauf Lehrstuhl für Mathematik (Mathematische Physik)

Involved external institutions

Novosibirsk State University (NSU) RU Russian Federation (RU)

How to cite

APA:

Knauf, A., & Taimanov, I.A. (2005). On the integrability of the n-centre problem. Mathematische Annalen, 331(3), 631--649. https://dx.doi.org/10.1007/s00208-004-0598-y

MLA:

Knauf, Andreas, and Iskander A. Taimanov. "On the integrability of the n-centre problem." Mathematische Annalen 331.3 (2005): 631--649.

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