Problem 111

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Central Limit Theorem for $\beta$-transform $x \mapsto (\beta x)$.

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Is there a survey on all that? What happened since [1]?


References

  1. [dolgopyat2004limit] Dolgopyat D.  2004.  Limit theorems for partially hyperbolic systems. Transactions of the American Mathematical Society. 356:1637–1689.

Central limit theorem, almost sure invariance principles, etc., for this and other interval maps, are in [1] and [2].


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