Statistical Mechanics, Magnetism, Quantum and Nonlinear DynamicsNo Access

ERGODICITY AND CHAOS IN A SYSTEM OF HARMONIC OSCILLATORS

M. HOWARD LEE

Department of Physics and Astronomy, University of Georgia Athens, GA 30602, United States of America

Korea Institute for Advanced Study, Seoul 130-012, Korea

https://doi.org/10.1142/S0217979209063213Cited by:2 (Source: Crossref)

Abstract

In recent years the term ergodicity has come into scientific vogue in various physical problems. In particular when a system exibits chaotic behavior, it is often said to be ergodic. Is it a correct usage of the term ergodicity? Does it not mean that the time and ensemble averages of a variable are equal? Are they really related one to one? We examine this issue via simple models of harmonic oscilators by means of the theorems of Birkhoff and Khinchin and also by our own physical theory of ergometry. This study also considers the chaotic behavior in the logistic map.

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