Jagiellonian University
Institute of Computer Science
and Computational Mathematics

The Home Page Of Daniel Wilczak

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Research interests:

Rigorous Numerical Analysis
Computer Assisted Proofs in Dynamical Systems
Qualitative Theory of Differential Equations
Dynamical Systems

Tutorial on Computer Assisted Proofs in Dynamics - presented at SWIM'2016 conference

1. Topological methods for ODEs: link

- 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

2. (Higher order) Variational methods for ODEs: link

- 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

3. Differential inclusions and dissipative PDEs: link

- 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.

CAPD library:

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