The entropy of alpha-continued fractions: analytical results
Dynamical Systems
2011-11-01 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.0912.2379,
title = {The entropy of alpha-continued fractions: analytical results},
author = {Giulio Tiozzo},
journal= {arXiv preprint arXiv:0912.2379},
year = {2011}
}
Comments
23 pages. The proofs are simpler than in the first version, and hold for all parameters