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

Abstract: 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.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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