论文标题
Rosen的中心限制持续分数
A Central Limit Theorem for Rosen Continued Fractions
论文作者
论文摘要
我们证明了Rosen持续分数算法的Birkhoff总和的中心限制定理。对于一般的一维持续分数获得了具有界限变化空间的一维持续分数，获得了Lasota-Yorke的结合，这意味着转移操作员的准混合度。主要的结果是直接证明了光谱间隙的存在，假设迭代时转换的某些行为。对于Rosen系统，明确证明了此条件。我们通过A. Broise的众所周知的结果得出结论，定理中心极限。
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.
