Colloquium Mathematics - Prof. Andreas Knauf

Title: Phase space compactification and regularisation for celestial bodies

Abstract:

In a joint work with Richard Montgomery (RCD, 2023) we compactify every energy surface for n bodies with homogeneous pair interaction, obtaining a manifold with corners in the sense of Melrose. After a time change, the flow on it is globally defined and is non-trivial on the boundary. This allows a detailed understanding of the dynamics at almost-collisions, and other asymptotics. A second topic will be regularisation by symplectic phase space extension for 2(1/n-1)-homogeneous potentials. Here n is an integer, n=2 corresponding to the Kepler potential, and the method works in any dimension (Nonlinearity, 2025).