September 22, 2020
September 22, 2020 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting
Understanding connecting and collision/ejection orbits is central to the study of transport in Celestial Mechanics. The atlas algorithm combines the parameterization method with rigorous numerical techniques for solving initial value problems in order to find and validate connecting orbits. However, difficulties arise when parameterizing orbits passing near a singularity such as “near miss” homoclinics or ejection/collision orbits. In this talk we present a method of overcoming this obstacle based on rigorous Levi-Civita regularization which desingularizes the vector field near the primaries. This regularization is performed dynamically allowing invariant manifolds to be parameterized globally, even near singularities.