α-连分数的熵：解析结果
The entropy of alpha-continued fractions: analytical results
摘要：
本文研究了由广义连分数算法产生的单参数区间映射族T_alpha的遍历论。首先证明了T_alpha的度量熵对参数α的依赖性是Hoelder连续的。此外，我们证明了一个中心极限定理可能无界的观测值的有界变化增长适度。这类函数足够大，可以覆盖Birkhoff平均收敛到熵的情况。
英文摘要：
We study the ergodic theory of a one-parameter family of interval maps T_alpha arising from generalized continued fraction algorithms. First of all, we prove the dependence of the metric entropy of T_alpha to be Hoelder-continuous in the parameter alpha. Moreover, we prove a central limit theorem for possibly unbounded observables whose bounded variation grows moderately. This class of functions is large enough to cover the case of Birkhoff averages converging to the entropy.
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