The \(n\)-centre problem of celestial mechanics for large energies (Q1599499)

The three-dimensional motion of a body in potential of \(n\) nuclei is addressed in the case of large energy \(E\). The author uses KS and Moller transformations to treat specific singularities. The analysis of symbolic dynamics is followed by an estimation of Hausdorff dimension and topological entropy of hyperbolic sets. The established methodologies are directly applicable to celestial mechanics, and form a basis for the study of molecular scattering by introducing an additional electronic potential. Approximation up to order \(1/E\) can be reached, but in the case of partial collinear configurations the author shows that the presented results are not valid.