CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

March 2, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Boundary value problems and transversality in conservative systems: computer assisted proofs of connection and collision orbits

Seminar presented by Jason D. Mireles James (Florida Atlantic University, USA)

I'll discuss a framework for two-point boundary value problems in conservative systems which detects transversality, allows for the possibility of multiple changes of coordinates, and leads naturally to computer assisted proofs.  The set-up applies to dynamical problems in the level set like finding connecting orbits between hyperbolic invariant objects and collisions.  The main technical difficulty is that the conserved quantity leads to overdetermined systems of equations.  This problem can be overcome in a number of different ways, including elimination of an equation, by exploiting discrete symmetries (if any), or by introducing a new variable called an unfolding parameter.   I'll look at two common ways of defining unfolding parameters and show that they don't disrupt the transversality properties of the BVP.  I'll also illustrate some applications of this setup to computer assisted proofs of connecting orbits and collisions in the circular restricted three body problem.  This is joint work with Shane Kepley and Maciej Capinski.