Scattering invariants in Euler's two-center problem
Mathematical Physics
2020-09-07 v1 math.MP
Abstract
The problem of two fixed centers was introduced by Euler as early as in 1760. It plays an important role both in celestial mechanics and in the microscopic world. In the present paper we study the spatial problem in the case of arbitrary (both positive and negative) strengths of the centers. Combining techniques from scattering theory and Liouville integrability, we show that this spatial problem has topologically non-trivial scattering dynamics, which we identify as scattering monodromy. The approach that we introduce in this paper applies more generally to scattering systems that are integrable in the Liouville sense.
Keywords
Cite
@article{arxiv.1801.09613,
title = {Scattering invariants in Euler's two-center problem},
author = {Nikolay Martynchuk and Holger R. Dullin and Konstantinos Efstathiou and Holger Waalkens},
journal= {arXiv preprint arXiv:1801.09613},
year = {2020}
}