The entropy of Nakada's α-continued fractions: analytical results
The entropy of Nakada's α-continued fractions: analytical results
We study the ergodic theory of a one-parameter family of interval maps T ↵ arising from generalized continued fraction algorithms.First of all, we prove the dependence of the metric entropy of T ↵ to be Hölder-continuous in the parameter ↵.Moreover, we prove a central limit theorem for possibly unbounded observables …