KO-4   Monday July 8 - 16:30

MS1 Part 2 of 2 - Computer-Assisted Proofs in Dynamics

MS1 Part 1 of 2

For many high and infinite dimensional dynamical systems it is not feasible to explore the dynamics in the entire phase space. One strategy to tackle this problem is to focus on a set of special solutions that act as organizing centers (for example because they form the skeleton of the attractor). To single out these solutions computer-assisted proofs are being developed to find, for example, fixed points, periodic orbits and connecting orbits between those. Rigorous numerics draws inspiration from scientific computing, nonlinear analysis, numerical analysis, applied topology, functional analysis and approximation theory. While in the past decade, these techniques have primarily been applied to ordinary differential equations, we are starting to witness their applicability for \emph{infinite dimensional} nonlinear dynamics generated by partial differential equations, integral equations, delay equations, and infinite dimensional maps. The purpose of this mini-symposium is to explore recent advances in this direction.

Blake Barker
Jean-Philippe Lessard

16:30 - 17:00 - Blake Barker - Rigorous verification of wave stability [Abstract]

17:00 - 17:30 - Maxime Breden - A computer-assisted study of the equilibria of a cross-diffusion system in population dynamics [Abstract]

17:30 - 18:00 - Jonathan Jaquette - Validated computation of infinite dimensional stable manifolds in a PDE [Abstract]

18:00 - 18:30 - Jean-Philippe Lessard - Rigorous integration for some infinite dimensional dynamical systems [Abstract]