Tutorial by Daniel Wilczak: Computer-assisted proofs in dynamics

Computer-assisted proofs in dynamics

Daniel Wilczak (Jagiellonian University, Krakow, Poland)

Sunday June 19

1 place de l'École, 69007 Lyon

Morning: 10h-12h

Afternoon: 14h-18h

The tutorial will make use of the CAPD library

1. Rigorous methods for ODEs

1a) Theory: rigorous methods for ODEs, Poincare maps

1b) Applications to dynamics: existence of attractors and chaos in ODEs, connecting orbits of special type (Shilnikov orbits, Bykov cycles), symmetric periodic orbits

1c) CAPD: introduction to ODE solvers and Poincare maps - live demo

 2. (Higher order) Variational methods for ODEs

2a) Theory: C^1-C^r-Lohner and C^1-Hermite-Obreschkov algorithms

2b) Applications to dynamics: Hamiltonian dynamics, branches of periodic orbits and their stability, connecting orbit between periodic orbits in ODEs, bifurcations of periodic orbits, invariant manifolds of periodic orbits

2c) CAPD: solvers for variational equations - live demo

3. Differential inclusions and dissipative PDEs

3a) Theory: algorithms for rigorous integration of differential inclusions and dissipative infinite dimensional systems.

3b) Applications: integration of differential inclusions, stable periodic orbits in PDEs, chaos in PDEs

3c) CAPD: solvers for differential inclusions - live demo