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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 2470-0045

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Identification Number: 10.1103/PhysRevE.51.3738


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
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Additional Information: © 1995 The American Physical Society
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Date Deposited: 26 Jan 2009 16:34
Last Modified: 17 Feb 2021 11:07

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