CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

22 septembre 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Computing and validating collisions, ejections, and homoclinics for the three body problem

Séminaire par Shane Kepley (Rutgers University, USA)

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.