Kolmogorov Arnold Moser Map

Sir Isaac Newton (best known for proposing the law of gravity in 1687) suggested a deterministic set of laws implying that the future is determined fully by the present. But since the mid-1970s, scientists have come to agree that determinism is transitory and may give way to chaotic behavior. Research at Los Alamos National Laboratory and a number of universities led to an understanding of the emergence of chaotic behavior in systems thought to be deterministic, a concept that has gained widespread acceptance in almost every discipline of science and mathematics. Early studies of nonlinear maps at Los Alamos led to the discovery of universality in the transition to chaos, described in the lab's most highly cited paper to date. This concept provides a fundamental understanding of the relationship between microscopic behavior of classical systems and macroscopic behavior dominated by statistical properties. Chaotic systems appear in many natural or engineered contexts. Strategies for control of such systems have been developed, with important implications for chemical engineering and fluid flow.

Scientific Impact: The concepts of chaos have changed how scientists view the dynamics in physical systems. In the early 1980s, few scientists believed in deterministic chaos; today, virtually all branches of science and engineering interpret nonrandom dynamics in the language of chaos, and all accept that chaos is an important advance in understanding of such systems.

Social Impact: These ideas have been implemented successfully in predicting nonlinear time series in financial markets, forecasting short-term weather, diagnosing and controlling medical conditions such as heart fibrillation, understanding stability in engineering structures and devices, and designing chaotic encryption schemes. Chaos theory also has changed, to some degree, the way the general public perceives science.

Reference: Feudel, U; Grebogi, C., "Multistability and the control of complexity," Chaos (Woodbury, N.Y.) Dec 31, 1997, ISSN 1054-1500.

Barreto, E; Hunt, B.R; Grebogi, C; Yorke, J.A., "From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space," Physical Review Letters, Jun 30, 1997, ISSN 0031-9007.

Auerbach, D.; Grebogi, C.; Ott, E.; Yorke, J.A., "Controlling chaos in high dimensional systems," Physical Review Letters, Dec 14, 1992, ISSN 0031-9007. Feigenbaum, M.J., "Quantitative universality for a class of nonlinear transformations," J. Stat. Phys., Jul 31, 1978.

Technical Contact: Daniel A. Hitchcock, Mathematical, Information, & Computational Sciences Division, 301-903-6767

Press Contact: Jeff Sherwood, DOE Office of Public Affairs, 202-586-5806

SC-Funding Office: Office of Advanced Scientific Computing Research