Von Zeipel's theorem on singularities in celestial mechanics
The classification of the singularities which can arise in the solutions of the classical n-body problem given by Painlevé (collisions and pseudocollisions) is used for the rigorous proof of Zeipel's theorem [\textit{H. von Zeipel}, Ark. Mat. Astron. Fys. 4, 32, 1-4 (1908)]. This theorem asserts that a noncollision singularity (a pseudocollision) can occur only if the system of particles (bodies) becomes unbounded in finite time. In the present paper von Zeipel's proof of the mentioned theorem is translated into modern mathematical notation and terminology. So the von Zeipel's remarkable original ideas become more readily available to current researchers.
scientific article; zbMATH DE number 4009869