Gaps in N-expansions

J. de Jonge, C. Kraaikamp, H. Nakada

For a natural number $N\ge 2$ and a real $\alpha$ such that $0<\alpha \le \sqrt{N}-1$, we define $I_{\alpha }:=[\alpha ,\alpha +1]$ and $I_{\alpha }^{-}:=[\alpha ,\alpha +1)$ and investigate the continued fraction map $T_α:I_α\to…