We show the ergodicity of Tanaka–Ito type $\alpha$-continued fraction maps and construct their natural extensions. We also discuss the relation between entropy and the size of the natural extension domain.
"On the Ergodic Theory of Tanaka–Ito Type $\alpha$-continued Fractions." Tokyo J. Math. Advance Publication 1 - 15, 2021. https://doi.org/10.3836/tjm/1502179343