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Global regularization for the $n$-center problem on a manifold
We describe a global version of the KS
regularization of the $n$-center problem on a closed 3-dimensional
manifold. The regularized configuration manifold turns out to be 4
or 5 dimensional closed manifold depending on whether $n$ is even
or odd. As an application, we show that the $n$ center problem in
$S^3$ has positive topological entropy for $n\ge 5$ and energy
greater than the maximum of the potential energy. The proof is
based on the results of Gromov and Paternain on the topological
entropy of geodesic flows. This paper is a continuation of
[6], where global regularization of the $n$-center
problem in $\mathbf R^3$ was studied.