Cookies?
Library Header Image
LSE Research Online LSE Library Services

Anomalous convergence of Lyapunov exponent estimates

Theiler, James and Smith, Leonard A. (1995) Anomalous convergence of Lyapunov exponent estimates. Physical Review E, 51 (4). pp. 3738-3741. ISSN 1539-3755

Full text not available from this repository.

Abstract

Numerical experiments reveal that estimates of the Lyapunov exponent for the logistic map xt+1=f(xt)=4xt(1-xt) are anomalously precise: they are distributed with a standard deviation that scales as 1/N, where N is the length of the trajectory, not as 1/ √N , the scaling expected from an informal interpretation of the central limit theorem. We show that this anomalous convergence follows from the fact that the logistic map is conjugate to a constant-slope map. The Lyapunov estimator is just one example of a ‘‘chaotic walk’’; we show that whether or not a general chaotic walk exhibits anomalously small variance depends only on the autocorrelation of the chaotic process.

Item Type: Article
Official URL: http://dx.doi.org/10.1103/PhysRevE.51.3738
Additional Information: © 1995 The American Physical Society
Library of Congress subject classification: Q Science > QA Mathematics
Q Science > QC Physics
Sets: Research centres and groups > Centre for the Analysis of Time Series (CATS)
Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 26 Jan 2009 16:34
URL: http://eprints.lse.ac.uk/22254/

Actions (login required)

Record administration - authorised staff only Record administration - authorised staff only