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| 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 |
