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

## 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 |
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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 |

Date Deposited: | 26 Jan 2009 16:34 |

URL: | http://eprints.lse.ac.uk/22254/ |

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