Dynamics of Algorithms

November 17 - 21, 1997

Emerging Applications of Dynamical Systems

Content

Overview

Organizers:

Jens Lorenz	University of New Mexico
Linda Petzold	University of California
Rafael de la Llave	The University of Texas at Austin

There are deep connections between the theory of algorithms and dynamical systems theory.

On one hand, the transformations of data effected by an algorithm can be considered as a dynamical system and the techniques of dynamical systems can be used to analyze properties such as global convergence, asymptotic rates, etc., and eventually lead to better numerical algorithms.

On the other hand, computations in dynamical systems present special challenges. For example, the objects to be discretized are geometric objects or have a very strong algebraic component. What is known a priori of the solutions affects the design of algorithms. Suitably designed algorithms may be used as ingredients in rigorous proofs.

Schedule

Monday, November 17, 1997

8:45 am - 9:15 am	Coffee and Registration	Keller 3-176
9:15 am - 9:30 am	Welcome and Orientation Rafael de la Llave (The University of Texas at Austin), Robert Gulliver, Willard Miller Jr.	Keller 3-180
9:30 am - 10:30 am	DAEs That Should not be Solved Uri Ascher (University of British Columbia)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Dynamics of DAE-Algorithms Roswitha Marz (Humboldt-Universität)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Representable Multivalued Maps as a Topological Bridge between Dynamics and Finite Mathematics Marian Mrozek (University of Krakow)	Keller 3-180

Tuesday, November 18, 1997

9:15 am - 9:30 am	Coffee	Keller 3-176
9:30 am - 10:30 am	Symmetry-Preserving Adaptive Integrators for Coulombic Few-Body Problems Benedict Leimkuhler (University of Kansas)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Conserving Algorithms on Lie Groups Debra Lewis (University of California)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Applications of Orthogonal Integration Techniques Erik Van Vleck (Colorado School of Mines)	Keller 3-180
3:00 pm - 4:00 pm	Complex Analysis Techniques for the Hánon Map Estela Gavosto (University of Kansas)	Keller 3-180
4:00 pm - 5:00 pm	Computation of Periodic Orbits Using Automatic Differentiation John Guckenheimer (Cornell University)	Keller 3-180

Wednesday, November 19, 1997

9:15 am - 9:30 am	Coffee	Keller 3-176
9:30 am - 10:30 am	Convergence Proofs for Numerical Software Andrew Stuart (Stanford University)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Multihomogeneous and Gauss-Newton Methods Michael Shub (IBM)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 2:20 pm	Complexity and Applications of Parametric Algorithms of Computational Algebraic Geometry Marek Rychlik (University of Arizona)	Keller 3-180
2:20 pm - 2:40 pm	Combinatorics of complex Hénon mappings Ricardo Oliva (CLT)	Keller 3-180
2:40 pm - 3:00 pm	Interval All Together Method for Parameter Identification George Corliss (Marquette University)	Keller 3-180
3:00 pm - 3:30 pm	Automatic Verification of Dynamical Systems Properties R. Baker Kearfott (University of Southwestern Louisiana)	Keller 3-180
3:30 pm - 4:00 pm	Net Math, a web-based computational tool William Schelter (The University of Texas at Austin)	Keller 3-180
4:00 pm - 4:15 pm	Coffee Break	Keller 3-176
4:15 pm - 5:00 pm	Computations with Gröbner Bases and Applications to Dynamical Systems Marek Rychlik (University of Arizona)	Keller 3-180

Thursday, November 20, 1997

9:15 am - 9:30 am	Coffee	Keller 3-176
9:30 am - 10:30 am	How do we Find out What a Dynamical System is Doing? James Yorke (University of Maryland)	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Scaling Laws for Shadowing Time Timothy Sauer (George Mason University)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Preservation Under Discretization of Invariant Rectangles for Solutions of Reaction-Diffusion Equations Donald Estep (Georgia Institute of Technology)	Keller 3-180

Friday, November 21, 1997

9:15 am - 9:30 am	Coffee	Keller 3-176
9:30 am - 10:30 am	Numerical Integration of Hamiltonian Systems with a Complex Solution Behavior Sebastian Reich (Konrad-Zuse-Zentrum für Informationstechnik (ZIB))	Keller 3-180
10:30 am - 11:00 am	Coffee Break	Keller 3-176
11:00 am - 12:00 pm	Asymptotic Expansions versus Backward Analysis for Numerical Integrators Ernst Hairer (Université de Genève)	Keller 3-180
12:00 pm - 2:00 pm	Lunch
2:00 pm - 3:00 pm	Integration of Matrix Equations: Orthonormal Integrators Luca Dieci (Georgia Institute of Technology)	Keller 3-180

Participants

Name	Department	Affiliation
Uri Ascher	Department of Computer Science	University of British Columbia
Elizabeth Bradley	Department of Computer Science	University of Colorado
Luigi Chierchia	Department of Mathematics	University of Rome 3
George Corliss	Department of Mathematics, Statistics and Computer Science	Marquette University
Rafael de la Llave	Department of Mathematics	The University of Texas at Austin
Amadeu Delshams	Departamento de Matematica Aplicada	Polytechnical University of Cataluña (Barcelona)
Luca Dieci	School of Mathematics	Georgia Institute of Technology
Donald Estep	School of Mathematics	Georgia Institute of Technology
Estela Gavosto	Department of Mathematics	University of Kansas
John Guckenheimer	Department of Mathematics	Cornell University
Ernst Hairer		Université de Genève
Daniel Henry	Lab. de Mecanique des Fluides et d'Acoustique	École Centrale de Lyon
Kathleen Hoffman	Institute for Mathematics and its Applications	University of Minnesota, Twin Cities
Joe Iwanski	Department of Applied Mathematics	University of Colorado
Miaohua Jiang	Department of Mathematics	Wake Forest University
Mark Johnson		NONE
Michael Jolly	Department of Mathematics	Indiana University
R. Baker Kearfott	Department of Mathematics	University of Southwestern Louisiana
Yohannes Ketema	Department of Aerospace Engineering and Mechanics	University of Minnesota, Twin Cities
Hans Koch	Department of Mathematics	The University of Texas at Austin
Bernd Krauskopf	Department of Engineering Mathematics	University of Bristol
Harbir Lamba	Division of Mechanics and Computation	Stanford University
Benedict Leimkuhler	Department of Mathematics	University of Kansas
Debra Lewis	Board of Mathematics	University of California
Jens Lorenz	Department of Mathematics & Statistics	University of New Mexico
Christian Lubich	Mathematisches Institut	Eberhard-Karls-Universität Tübingen
Mitchell Luskin	School of Mathematics	University of Minnesota, Twin Cities
Kurt Lust	Center for Applied Mathematics	Cornell University
Rolf-Martin Mantel	Institute for Mathematics and its Applications	University of Minnesota, Twin Cities
Roswitha Marz	Institute for Mathematics	Humboldt-Universität
Gianfranco Mascari	Istituto per le Applicazioni del Calcolo (IAC)	University of Naples / CNR
Marian Mrozek		University of Krakow
Rolf Neubert	ZT AN 2	Siemens AG
Ricardo Oliva		CLT
Peter Olver	School of Mathematics	University of Minnesota, Twin Cities
Linda Petzold	Department of Mechanical and Envinronmental Engineering	University of California
Thomas Posbergh	Department of Aerospace Engineering and Mechanics	University of Minnesota, Twin Cities
Sebastian Reich		Konrad-Zuse-Zentrum für Informationstechnik (ZIB)
Marek Rychlik	Department of Mathematics	University of Arizona
Bjorn Sandstede	Department of Mathematics	The Ohio State University
Timothy Sauer		George Mason University
William Schelter	Department of Mathematics	The University of Texas at Austin
Dieter Schmidt	Department of Mathematics	University of Cincinnati
Tony Shardlow	Institute for Mathematics and its Applications	University of Minnesota, Twin Cities
Michael Shub		IBM
Andrew Stuart	Computer Science and Mechanical Engineering	Stanford University
Peter Szmolyan	Institut fur Angewandte und Numerische Mathematik	Technische Universität Wien
Andrzej Szymczak	Department of Mathematics	Georgia Institute of Technology
Erik Van Vleck	Department of Mathematics and Computer Science	Colorado School of Mines
Robert Warnock		SLAC
Shinya Watanabe	Department of Mathematics and Informatics	Ibaraki University
James Yorke	Institute for Physical Science and Technology	University of Maryland
Guocheng Yuan	Department of Mathematics	University of Maryland