CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

December 3, 2020 from 11:15 to 11:30 (Montreal/EST time) Zoom meeting

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

Seminar presented by 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.