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I was looking for information about the correlation decay of the logistic map, more precisely if there is any parameter for which its decay is subexponential, in which case I would like to know if it can exhibit intermittency. I found the article Chaotic maps with slowly decaying correlations and intermittency which can be found on researchgate, and in section 3.2 when the author talks about the logistic map it is said that

[...] and there is also a subset of values of $\theta$ for which the rate of decay of correlations is subexponential, see Bruin, Luzzatto and van Strien.

The article mentioned is Decay of correlations in one-dimensional dynamics and $\theta$ is the parameter of the logistic map $f(x)=\theta x(1-x)$. The article can be found on arxiv as well.

So I don't quite understand how the cited reference guarantees that there are parameters for which the decay of correlations is subexponential. Could anyone tell me which result of the article was used and if there would be any additional references.

In the abstract of the article by Bruin, Luzzatto and van Strien it is said

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.

I didn't find exactly this result in the article (maybe corollary 1.1), but the logistic map is a quadratic Fibonacci map?

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    $\begingroup$ I believe the term subexponential is being used in a strange way here. I think they’re giving results on mixing of the unimodal map, showing that it mixes “at least polynomially fast”. I don’t think they are showing that it does not mix exponentially fast. (I.e. they prove sub-exponential lower bounds, but no upper bounds on the rate of mixing). $\endgroup$
    – Anthony Quas
    Commented Aug 16, 2022 at 1:48
  • $\begingroup$ @AnthonyQuas I thought something similar, but since the article by Bhansali, Holland and Kokoszka says that decay is subexponential, I thought I might be missing something in the article they cited. $\endgroup$
    – Mrcrg
    Commented Aug 17, 2022 at 15:56

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