Jagiellonian University The Home Page Of Daniel Wilczak |
Rigorous Numerical Analysis
Computer Assisted Proofs in Dynamical Systems
Qualitative Theory of Differential Equations
Dynamical Systems
- Theory: Rigorous methods for ODEs, Poincare maps
- Applications: existence of attractors and chaos in ODEs, connecting orbits of special type (Shilnikov orbits, Bykov cycles), symmetric periodic orbits
- Theory: C1-Cr-Lohner and C1-Hermite-Obreschkov algorithms
- Applications: 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
- Theory: algorithms for rigorous integration of differential inclusions and dissipative infinite dimensional systems.
- Applications: integration of differential inclusions, stable periodic orbits in PDEs, chaos in PDEs
I recommend to download the tutorial as a single archive. It contains all three presentations, C++ sources of the programs, two animations and a movie.
All examples of computer-assisted proofs from the tutorial are based on the CAPD library.
SWIM 2016 - 9th Summer Workshop on Interval Methods
June 19-22, 2016, Lyon, France
Workshop on Computational Dynamics
April 4-8, 2016, Providence, USA
Winter School on Computational Mathematics
February 7-13, 2016, Bedlewo, Poland
Dynamics, Topology and Computations
June 15-20, 2015, Będlewo, Poland
SWIM 2015 - 8th Small Workshop on Interval Methods
June 9-11, 2015, Prague, Czech Republic
Foundations of Computational Mathematics 2014,
Workshop:
Computational Dynamics
December 11-20, 2014, Montevideo, Uruguay
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications,
July 7-11, 2014, Madrid, Spain
SWIM 2014 - 7th Small Workshop on Interval Methods
June 11-12, 2014, Uppsala, Sweden
Dynamics, Topology and Computations
June 24-30, 2012, Będlewo, Poland
Symposium on Nonlinear Analysis
September 7-9, 2011, Toruń, Poland
Computational Methods in Dynamics
July 4-8, 2011, Triest, Italy
Foundations of Computational Mathematics 2011,
Workshop:
Computational Dynamics
July 4-14, 2011, Budapest, Hungary