Short Course on Chaos: Theory and Numerics
Organizer: James A. Yorke, Institute for Physical Science and Technology
University of Maryland, College Park
Saturday, May 20, 1995
Snowbird Ski and Summer Resort
The first half of this short course will deal with simple models of chaotic behavior in one and two dimensions. James Yorke and Robert Devaney will describe the transition to chaos that many types of systems undergo. Using symbolic dynamics, they will describe the dynamics of a "typical" chaotic system. Finally, using specific examples drawn from real and complex dynamics, they will show how these simple models allow us to understand the chaotic behavior that arises in more complicated settings.
The second half of the course will discuss the numerics of chaos. Sensitivity to initial data is a hallmark of the field and this suggests that numerical investigations of chaotic systems are inherently unreliable. The afternoon will concentrate on how to make reliable numerical studies with emphasis on dynamics in the plane and how to explore the behavior of a dynamical system.
Specific topics to be discussed include chaotic trajectories, basins of attraction, bifurcations, period doubling cascades, the Feigenbaum scenario, the shift map and the sequence space, stable manifolds and homoclinic points and the Henon map and the forced damped pendulum.
The course is 15% introductory, 75% intermediate, and 10% advanced.
Objectives and Rationale
This is an introduction to some of the central themes about which the following meeting is centered. People of many backgrounds will attend the SIAM Conference. This course will act to strengthen their backgrounds in certain core themes of dynamics. The goal is to introduce the audience to a number of central themes in non-linear dynamics.
Robert L. Devaney received his A.B. from Holy Cross College and his PhD from the University of California at Berkeley in l973 and is now at Boston University. He served as Chair of the Department of Mathematics from l983-l986. He has authored two books and produced a number of short films on dynamical systems. He has delivered over 500 lectures both nationally and abroad and has authored over 50 research papers in the field of dynamics.
James A. Yorke received his A.B. from Columbia University and his PhD from the University of Maryland in 1966, where he is the Director of the Institute for Physical Science and Technology, a research department consisting of about 30 chemists, mathematicians, physicists, and engineers. He coined the term "chaos" as a mathematical concept in non-linear dynamics. He has co-authored over 200 papers, authored 3 books, and has presented over 300 lectures nationally and abroad.
Who Should Attend?
This course should be accessible to graduate students in mathematics and physics and researchers in other disciplines. We will restrict attention to the simpler case of discrete dynamical systems, so attendees need not have a great deal of acquaintance with dynamical systems theory.
Background would be some familiarity with dynamics as found for example in the first 6 - 9 chapters of R.L. Devaney's book, "A First Course in Chaotic Dynamical Systems," published by Addison-Wesley.
Short Course Program
8:00 AM ~ Registration
9:00 AM-10:30 AM ~ Introduction to Chaos, Robert L. Devaney
10:30 AM-11:00 AM ~ Coffee
11:00-AM-12:30 PM ~ Introduction to Chaos (continued) , Robert L. Devanay
12:30 PM-2:00 PM ~ Lunch
2:00 PM-3:30 PM ~ Introduction to the Numerics of Chaos, James L. Yorke
3:30 PM-4:00 PM ~ Coffee
4:00 PM-5:30 PM ~ Introduction to the Numerics of Chaos (continued), James L. Yorke
5:30 PM ~ Short Course adjourns
Click here for Short Course registration information.