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.

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