59 citations · 177 across the 25 of their papers we have counts for
26 papers
Compactification of the energy surfaces for n bodies
Andreas Knauf, Richard Montgomery
For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimension…
Classical -body scattering with long-range potentials
Jacques Féjoz, Andreas Knauf, Richard Montgomery
We consider the scattering of classical particles interacting via pair potentials, under the assumption that each pair potential is "long-range", i.e. being of order ${\cal O}(…
Topology change of levels sets in Morse theory
Andreas Knauf, Nikolay Martynchuk
Classical Morse theory proceeds by considering sublevel sets of a Morse function , where is a smooth finite-dimensional manifold. In this paper…
Asymptotic velocity for four celestial bodies
Andreas Knauf
Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proven for bounded interaction potentials. This is known to be wrong in celestial me…
Improbability of Wandering Orbits Passing Through a Sequence of Poincaré Surfaces of Decreasing Size
Stefan Fleischer, Andreas Knauf
Given a volume preserving dynamical system with non-compact phase space, one is sometimes interested in special subsets of its wandering set. One example from celestial mechanics i…
Improbability of Collisions in -Body Systems
Stefan Fleischer, Andreas Knauf
For a wide class of two-body interactions, including standard examples like gravitational or Coulomb fields, we show that collision orbits in -body systems are of Liouville meas…