On cycles for the doubling map which are disjoint from an interval

Kevin G. Hare, Nikita Sidorov

Let $T:[0,1]\to [0,1]$ be the doubling map and let $0<a<b<1$. We say that an integer $n\ge 3$ is bad for $(a,b)$ if all $n$-cycles for $T$ intersect $(a,b)$. Let $B(a,b)$ denote the…