On the integrability of the n-centre problem

Details On the integrability of the n-centre problem On the integrability of the n-centre problem

2004-01-16

arxiv.org/abs/math/0401202v1

Mathematische Annalen 331 (2005), 631--649

Mathematics

Dynamical Systems

22 pages, a short announcement see in math.DS/0312429

Scientific paper

It is known that for $n \geq 3$ 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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