The entropy of alpha-continued fractions: analytical results

Details The entropy of alpha-continued fractions: analytical results The entropy of alpha-continued fractions: analytical results

2009-12-13

arxiv.org/abs/0912.2379v2

Mathematics

Dynamical Systems

23 pages. The proofs are simpler than in the first version, and hold for all parameters

Scientific paper

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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