Thursday, August 10
MS18
Computational Topology and Geometry in Analysis of ODE's and Time Series
1:00 PM-3:00 PM
Hibiscus & Ilima (Salon 3 & 4)
This minisymposium will focus on recent developments in the numerical analysis of ODE's and time series using methods from computational topology and geometry, as well as applications to fourth-order ODE's arising in pattern formation problems. The main dynamical tool used to apply computational homology algorithms and computational geometry constructions, such as Delaunay triangulations, is the Conley index. The speakers will address the structure of solutions, including braided solutions and traveling waves, to classes of fourth-order ODE's based on computational results for the Conley index.
Organizers: William D. Kalies
Florida Atlantic University, USA
Vivi Rottschäfer-Keijser
Boston University, USA
Robert VanderVorst
Leiden University, The Netherlands
- 1:00-1:25 Abundance of Homoclinic and Heteroclinic Orbits for the
Henon-Heiles
Hamiltonian. A Computer Assisted Proof
- Piotr Zgliczynski, Jagiellonian University, Cracow,
Poland
and Indiana University
- 1:30-1:55 Axisymmetric Solutions in the 2-D Gray-Scott Model
- Dave Morgan, Boston University
- 2:00-2:25 Existence and Stability of Traveling Fronts in the Extended Fisher-Kolmogorov Equation
- Vivi Rottschäfer-Keijser, Organizer; and C. E. Wayne, Boston University, USA
- 2:30-2:55 Simplicial Approximation and Conley Index Computations for Flows
- Erik Boczko, Georgia Institute of Technology, USA; William Kalies, Organizer; and Konstantin Mischaikow, Georgia Institute of Technology, USA