DMCA
Decay of Correlations in One-Dimensional Dynamics (2002)
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@MISC{Bruin02decayof,
author = {Henk Bruin and Stefano Luzzatto and Sebastian Van Strien},
title = {Decay of Correlations in One-Dimensional Dynamics },
year = {2002}
}
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Abstract
We consider multimodal C³ interval maps f satisfying a summability condition on the derivatives Dn along the critical orbits which implies the existence of an absolutely continuous f-invariant probability measure µ. If f is non-renormalizable, µ is mixing and we show that the speed of mixing (decay of correlations) is strongly related to the rate of growth of the sequence (Dn) as n → ∞. We also give sufficient conditions for µ to satisfy the Central Limit Theorem. This applies for example to the quadratic Fibonacci map which is shown to have subexponential decay of correlations.
