The entropy of alpha-continued fractions: analytical results

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.

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

Cited by in corpus (3)

• Cross sections for geodesic flows and α-continued fractions
• Dynamics of continued fractions and kneading sequences of unimodal maps
• A Central Limit Theorem for Rosen Continued Fractions