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arXiv · 0912.2379

The entropy of alpha-continued fractions: analytical results

Giulio Tiozzo
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Abstract

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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Giulio Tiozzo. 2011-10-31. The entropy of alpha-continued fractions: analytical results. https://arxiv.org/abs/0912.2379

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