For his contributions to the field of dynamical systems, John Guckenheimer, the A.R. Bullis Professor of Mathematics, was awarded the 2013 AMS Leroy P. Steele Prize for Mathematical Exposition. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics.
The prize was awarded Jan. 10 at the society’s meetings in San Diego. Also honored with the prize was Guckenheimer’s co-author, Philip Holmes of Princeton University.
Guckenheimer and Holmes were honored for their book, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields” (Springer-Verlag, 1983), the first treatise on the modern theory of dynamical systems. It explores the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations.
The understanding of dynamical systems underwent a rebirth in the 1960s and 1970s thanks to mathematicians and other theoreticians, and applied scientists such as engineers and experimental physicists, the prize citation says. “Not surprisingly, it was difficult for the two communities to know about each other’s work until the publication of the now-classic text by Guckenheimer and Holmes. Thirty years later this book remains in wide use as a standard text for graduate-level courses in mathematics departments and throughout the sciences and engineering, and Chinese and Russian translations have appeared,” the citation said.
The authors met in 1976 when rapid advances in dynamical systems theory were stimulating experimental work that demonstrated the usefulness of the theory in explaining empirical phenomena across the sciences and engineering, Guckenheimer said. “We saw a real need for a book that made the new mathematics accessible to a broad audience,” he said. “We tried hard to explain mathematical concepts and arguments in their simplest manifestations while relying on as little formal training as seemed feasible. It helped that we came to the interface between mathematics and the physical sciences from opposite sides.”
During the past 15 years, Guckenheimer’s research has investigated dynamical systems with multiple time scales and associated numerical methods. He has also continued to investigate the use of dynamical systems theory in diverse areas, notably in neuroscience and animal locomotion. He was a 1984 Guggenheim fellow and is a fellow of the American Academy of Arts and Sciences, the American Association for Advancement of Science, the American Mathematical Society, and the Society for Industrial and Applied Mathematics, where he served as president 1997-98.