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Numerical Methods for Bifurcation Problems
September 15 - 19, 1997


Wolf-Jürgen Beyn, Universität Bielefeld
Eusebius Doedel,
Concordia University  (Chair)
Bernold Fiedler, Free University of Berlin
Yannis Kevrekedis, Princeton University
Jens Lorenz, University of New Mexico

While computational techniques for low-codimension local bifurcations in few-degree-of-freedom systems are in advanced state of development, much work remains to be done on the numerical treatment of higher-codimension singularities. More importantly, there is a pressing need for the development of numerical methods for computing global objects in phase space, their interactions and bifurcations.

For this workshop we brought together mathematicians, numerical analysts and computer scientists working on these problems, and studied a selected set of important applications. Particular topics considered included the numerical computation of invariant manifolds (including invariant tori, homoclinic and heteroclinic manifolds as well as inertial manifolds), the detection of their bifurcations and their visualization.

The Geometry Center was involved in this workshop.

Click on the titles to find abstracts and/or links to presentation materials

W. Miller, R. Gulliver,
E. Doedel
Welcome and Orientation
Bjorn Sandstede,
Ohio State University
Numerical computation of pulses and their dynamics
Andrey Shilnikov,
Inst. Appl. Math & Cybernetics
Qualitatively numerical analysis of some concrete models with non-trivial dynamics
Dimitri Turaev,
Weizmann Institute
Branching homoclinic orbits in Hamiltonian systems
Short Talks
Mercé Ollé,
Univ. Politécnica
Numerical Exploration of Bifurcation Phenomena Associated to Complex Instability
Timothy J. Burns,
On the Bifurcation from Continuous to Segmented Chip Formation in Metal Cutting
Gerald Moore,
Imperial College, London
Different Algorithms for Connecting Orbits
Hinke Osinga,
University of Minnesota
Globalizing two-dimensional unstable manifolds
Eric Kostelich,
Arizona State University
Calculating Stable and Unstable Manifolds
Konstantin Mischaikov,
Georgia Institute of Technology
Computer-Assisted Exploration and Proof in Dynamics
Michael Dellnitz,
University of Bayreuth
The Approximation of Complicated Dynamical Behavior
Vemuri Balakotaiah,
University of Houston
Numerical Bifurcation Techniques for Chemical Reactor Problems
Yannis Kevrekidis,
Princeton University
A computer-assisted study of reaction-diffusion patterns in microcomposite media
Ray Adomaitis,
University of Maryland
Numerical Continuation of Bifurcations and Global Dynamic Behavior Transitions for a Noninvertible System
Alastair Spence,
University of Bath
Numerical methods for detecting Hopf points and computing periodic orbits in large systems
Patrick Miller,
Brown University
Using Invariant Manifolds to Characterize Transport in Numerically-Generated Velocity Fields
Jens Lorenz,
Georgia Tech
Self Organized Criticality: A Sandpile Model
Luca Dieci,
Georgia Tech
On Smooth Decomposition of Matrices
Yuri A. Kuznetsov,
CWI/RIACA, Amsterdam
Normal form computations in CONTENT
Mark Levi,
Rensselaer Polytechnic Institute
Curvature effects in the averaging of high-frequency vibrations
Don Aronson,
University of Minnesota
Dynamics of Josephson Junctions Coupled through a Shared LRC-Load
James A. Yorke,
University of Maryland
Discontinuous Bifurcations for Dissipative Maps in the Plane

A joint talk with the Midwest Dynamical Sytems Conference


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1997-1998 Emerging Applications of Dynamical Systems