Note to users. If you're seeing this message, it means that your browser cannot find this page's style/presentation instructions -- or possibly that you are using a browser that does not support current Web standards. Find out more about why this message is appearing, and what you can do to make your experience of our site the best it can be.

Science 13 January 1989:
Vol. 243. no. 4888, pp. 182 - 187
DOI: 10.1126/science.243.4888.182
Prev | Table of Contents | Next

Articles

Ergodic Theory, Randomness, and "Chaos"

D. S. ORNSTEIN 1

1 Professor of mathematics at Stanford University, Stanford, CA 94305.

Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.


THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
Justifying Definitions in Mathematics--Going Beyond Lakatos.
C. Werndl (2009)
Philosophia Mathematica 17, 313-340
   Abstract »    Full Text »    PDF »
References for Simulation & Gaming, Vol. 25, No. 4.
(1994)
Simulation Gaming 25, 536-544
Structure, Indeterminacy and Chaos: A Case for Sociological Law.
R. Huckfeldt (1990)
Journal of Theoretical Politics 2, 413-433
   Abstract »


To Advertise     Find Products

Science. ISSN 0036-8075 (print), 1095-9203 (online)