Survivor Set of Gauss Map with a Hole at $1$

Cheng Liu, Lingmin Liao

Let $T$ be the Gauss map. For each $\alpha \in [0,1]$, let $E(\alpha )$ be the survivor set consisting of all $x\in [0,1]$ whose orbit $\{T^k(x):k\ge 0\}$ never enters the interval $(\alpha ,1]$. We…