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Decay of correlations in one-dimensional dynamics

Henk Bruin·Stefano Luzzatto·Sebastian van Strien
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Abstract

We consider multimodal C^3 interval maps f satisfying a summability condition on the derivatives D_n along the critical orbits which implies the existence of an absolutely continuous f -invariant probability measure mu. If f is non-renormalizable, mu is mixing and we show that the speed of mixing (decay of correlations) is strongly related to the rate of growth of the sequence D_n as n tends to infinity . We also give sufficient conditions for mu to satisfy the Central Limit Theorem. This applies for example to the quadratic Fibonacci map which is shown to have subexponential decay of correlations.

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Henk Bruin, Stefano Luzzatto, Sebastian van Strien. 2002-08-14. Decay of correlations in one-dimensional dynamics. https://arxiv.org/abs/math/0208114

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