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Organizers:
Fred Dumortier, Limburgs Universitair Centrum
Chris Jones, Brown University (Chair)
Alexander Khibnik, Cornell University
David Terman, Ohio State
Steve Wiggins, Caltech
Many physical problems, particularly in chemical and biological systems, involve processes that occur on widely varying time scales. The resulting model is a system that has a singular perturbation character. Such problems have motivated the development of much mathematical theory, including classical asymptotic theory and a geometric theory based on invariant manifolds. The phenomena that appear in singular-perturbation problems are subtle, often involving expansions in terms of quantities that are exponentially small in terms of a small parameter in the problem. The singular structure of these equations can also pose formidable numerical challenges. The goal of this workshop was to explore the connection between the asymptotic and geometric theories, with a particular emphasis on exponentially small phenomena, and to bring researchers developing these methods together with people working on applications in biology, chemistry and mechanics.
Click on the titles to find abstracts and/or links to presentation materials
MONDAY, OCTOBER 27 | ||
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W. Miller, R. Gulliver, C. Jones |
Welcome and Orientation | |
David McLaughlin, Courant Institute, NYU |
Chaotic and Homoclinic Behavior in PDE's | |
Nigel Goldenfeld, University of Illinois |
Renormalization Group Approach to Global Asymptotic Analysis | |
Amadeu Delshams, Univ. Politécnica de Catalunya |
Homoclinic orbits to invariant tori in Hamiltonian Systems | |
Richard Haberman, Southern Methodist Univ. |
Slow passage through a homoclinic orbit with subharmonic resonances | |
Alexandra Milik, Techn. Univ. of Vienna |
The Geometry of Mixed-mode Oscillations in a Chemical Oscillator | |
TUESDAY, OCTOBER 28 | ||
Konstantin Mischaikow, Georgia Institute of Technology |
A topological approach to fast-slow dynamics | |
Michael J. Davis, Argonne National Laboratory |
Some Multiple-Time-Scale Problems in Chemical Dynamics, Molecular Spectroscopy, & Kinetic Modeling | |
Linda Petzold, University of California-Santa Barbara |
Model Reduction for Nonlinear Dynamical Systems from Chemical Kinetics | |
Michael Ward, University of British Columbia |
Dynamic Metastability for Reaction-Diffusion Equations | |
Xiao-Biao Lin, North Carolina State University |
Method of singular characteristics for Hamilton-Jacobi equations that develop shock structures | |
Mohammed Ziane, Stanford University |
A mathematical formulation of the Goldenfeld renormalization group method | |
Jiangzhong Su, Univ. of Texas at Arlington |
Delay of bifurcation phenomena and their analysis | |
WEDNESDAY, OCTOBER 29 | ||
Anatoly Neishtadt, Space Research Institute, Moscow |
On stability loss delay f or dynamical bifurcations | |
Robert A. Gardner, University of Massachusetts |
Stability Analysis of Singular Patterns for the 1-D Gray-Scott Model | |
David Terman, Ohio State University |
Multiple Time Scales in Networks of Neural Oscillators | |
Tasso Kaper, Boston University |
Exchange lemmas: an overveiew and some new applications | |
THURSDAY, OCTOBER 30 | ||
Chongchun Zeng, Courant Institute, NYU |
Invariant Manifolds and Invariant Foliations for Semiflows in Banach Space | |
Yulij Ilyashenko, Cornell University/ Moscow State & Indep. Universities |
Embedding theorems for maps and normal forms for the slow-fast systems | |
George Haller, Brown University |
Homoclinic jumping in evolution equations | |
Robert Roussarie, University of Bourgogne |
Multiple Canard Cycles in Van Der Pol-like Equations | |
Pavol Brunovsky, Cornenius University |
C^{k} inclination theorems for singularly perturbed problems | |
Peter Szmolyan, Technische Universität Wein |
Extending Geometric Singular Perturbation Theory to Non-hyperbolic Points | |
Discussion Session | Panel: Marc Diener, Freddy Dumortier, Paul Fife, Chris Jones, David McLaughlin | |
FRIDAY, OCTOBER 31 | ||
Petar Kokotovic, University of California-Santa Barbara |
Singular Perturbations and Multiple Time Scales in Control System Modeling and Design | |
Dennis Perchak, Kodak |
This talk is joint with the IMA Seminar on Industrial
Problems:
Stokesian Dynamics Simulation of Interacting Solid Particles |
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