Intermediate Length Scale Effects in Lyapunov Exponent Estimation
Algorithms for estimating Lyapunov exponents from experimental data monitor the divergence of nearby phase space orbits. These algorithms rely on the assumption that the dynamics on intermediate length scales are “close” to the dynamics on infinitesimal length scales. We have studied two one-dimensional maps in which intermediate length scale dynamics may result in inaccurate exponent estimates. This effect is found to be small enough so that the exponent estimates are still good characterizations of the systems. Similar effects are likely to be present whenever a finite quantity of data is used for Lyapunov exponent estimation.
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- 3.More precisely we should say that the long-term growth rate of δx(t) is λ1 For the 1−D map these definitions are equivalent, but in higher dimensions the transient behavior of the vector δx(t) will almost always depend on other Lyapunov exponents.Google Scholar
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