The Entropy of Nakada’s Α-continued Fractions: Analytical Results
نویسنده
چکیده
We study the ergodic theory of a one-parameter family of interval maps Tα arising from generalized continued fraction algorithms. First of all, we prove the dependence of the metric entropy of Tα to be Hölder-continuous in the parameter α. 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. MSC: 11K50, 37A10 (Primary) 37A55, 37E05 (Secondary)
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تاریخ انتشار 2011