Global regularization for the $n$-center problem on a manifold

Sergey V. Bolotin; Piero Negrini

doi:10.3934/dcds.2002.8.873

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2002, Volume 8, Issue 4: 873-892. Doi: 10.3934/dcds.2002.8.873

This issue Previous Article On uniqueness of positive solutions for a class of semilinear equations Next Article Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data

Global regularization for the $n$-center problem on a manifold

Sergey V. Bolotin^1, and
Piero Negrini^2,

1.
Department of Mathematics, University of Wisconsin, Madison
2.
Department of Mathematics, La Sapienza, University of Rome

Received: July 31, 2001

Revised: January 31, 2002

Published: September 2002

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Abstract

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.

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Mathematics Subject Classification: 37B40, 37J15, 27J30, 70F16.

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