KO-4   Monday July 8 - 14:00

MS1 Part 1 of 2 - Computer-Assisted Proofs in Dynamics

MS1 Part 2 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

14:00 - 14:30 - Michael Plum - Computer-assisted existence and multiplicity proofs for semilinear elliptic boundary value problems [Abstract]

14:30 - 15:00 - Jason Mireles James - The parameterization method, transverse intersections, and computer assisted proof in celestial mechanics [Abstract]

15:00 - 15:30 - Sarah Day - Sofic shifts via Conley index theory: computing lower bounds on recurrent dynamics for maps [Abstract]

15:30 - 16:00 - Akitoshi Takayasu - Rigorous numerics for nonlinear heat equations in the complex plane of time [Abstract]