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Newton's Method, Circle Maps, and Chaotic Motion

by Donald G. Saari and John B. Urenko

Year of Award: 1985

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 91, 1984, pp. 3-17

Summary: This article shows that even though the sequences that arise from Newton's method comprise a deterministic system, there are subsystems that have highly random behavior in a specific sense.

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About the Authors: (from The American Mathematical Monthly, vol. 91 (1984))

Donald G. Saari  received his Ph.D. from Purdue University under Harry Pollard. After a postdoctoral position in the Yale Astronomy Department, he moved to Northwestern where he is professor of mathematics. His research interests include celestial mechanics, dynamical systems, and the information theory associated with mathematical economics.

John B. Urenko is an assistant professor of mathematics at the Schuylkill Campus of the Pennsylvania State University. He received his Ph.D. in 1975 at Northwestern University, working in celestial mechanics under D. Saari. He has taught in the mathematics departments of the University of Illinois at Chicago Circle and Loyola University of Chicago. His primary mathematical interests are celestial mechanics and dynamical systems.


Subject classification(s): Differential & Difference Equations | Dynamical Systems | Algebraic Numbers
Publication Date: 
Tuesday, September 23, 2008