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A Central Limit Theorem for Rosen Continued Fractions

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arxiv 2009.02047 v2 pith:3E7NNQ4F submitted 2020-09-04 math.DS

A Central Limit Theorem for Rosen Continued Fractions

classification math.DS
keywords centralcontinuedlimitrosentheoremfractionsalgorithmassuming
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We prove a central limit theorem for Birkhoff sums of the Rosen continued fraction algorithm. A Lasota-Yorke bound is obtained for general one-dimensional continued fractions with the bounded variation space, which implies quasi-compactness of the transfer operator. The main result is a direct proof of the existence of a spectral gap, assuming a certain behavior of the transformation when iterated. This condition is explicitly proved for the Rosen system. We conclude via well-known results of A. Broise that the central limit theorem holds.

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