Resource title

Anomalous convergence of Lyapunov exponent estimates

Resource image

image for OpenScout resource :: Anomalous convergence of Lyapunov exponent estimates

Resource description

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.

Resource author

Resource publisher

Resource publish date

Resource language

en

Resource content type

Resource resource URL

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

Resource license