A new class of $\alpha$-Farey maps and an application to normal numbers

Karma Dajani, Cornelis Kraaikamp, Hitoshi Nakada +1

We define two types of the $\alpha$-Farey maps $F_{\alpha }$ and $F_{\alpha ,♭}$ for $0<\alpha <\frac{1}{2}$, which were previously defined only for $\frac{1}{2}\le \alpha \le 1$ by R.~Natsui (2004).…