Friday, August 11

MS35
Computational Topological Dynamics

1:30 PM-3:30 PM
Hibiscus & Ulima (Salon 3 & 4)

The goal of computational topological dynamics is to provide a numerical approach to the study of dynamical systems by topological tools. Topological methods lead to relatively inexpensive algorithms and provide stable results. With additional computational effort the results may be turned into computer assisted proofs. The methods involved include algebraic topology, Conley and fixed point indices and rigorous numerical analysis. The speakers in this minisymposium will concentrate on algorithms computing homology, enclosing unstable manifolds and enclosing solutions of differential equations. They will present concrete applications in dynamics.

1:30-1:55 Adaptive Computational Tools for Invariant Sets

Michael Dellnitz, University of Paderborn, Germany

2:00-2:25 Computing Homology of a Continuous Map

Tomasz Kaczynski, Université de Sherbrooke, Canada

2:30-2:55 Some Recent Results in Computer Assisted Proofs in Dynamics

Marian Mrozek, Organizer

3:00-3:25 New Topological Method for Rigorous Study of Dynamics of Dissipative PDE's. Rigorous Results about Kuramoto- Sivashinsky Equations

Piotr Zgliczynski and Konstantin Mischaikow, Georgia Institute of Technology, USA