CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

3 décembre 2020 de 11 h 15 à 11 h 30 (heure de Montréal/HNE) Réunion Zoom

CRM-CAMP SPOTLIGHT ON GRADUATE RESEARCH: Parameterized invariant manifold and applications in celestial mechanics

Séminaire par Maxime Murray (Florida Atlantic University, USA)

The parameterization method is a well-known framework with proven value to parameterize hyperbolic manifolds attached to periodic solutions of ordinary differential equations. Using a Taylor expansion, one can rewrite the computation of the manifold into a recursive system of linear differential equations describing the coefficients. I will discuss this approach and how to obtain an interval enclosure of the truncated solution to the system. I will then show how validated manifolds are used to compute cycle-to-cycle connections in the case of the circular restricted three-body problem and Hill's four-body problem.