The doubling map with asymmetrical holes

Paul Glendinning, Nikita Sidorov

Let $0<a<b<1$ and let $T$ be the doubling map. Set $\mathcal{J}(a,b):=\{x\in [0,1]:T^{n}x\notin (a,b),n\ge 0\}$. In this paper we completely characterize the holes $(a,b)$ for which…