Shrinking random $\beta$-transformation

Kan Jiang, Karma Dajani

For any $n\ge 3$, let $1<\beta <2$ be the largest positive real number satisfying the equation $${\beta }^n={\beta }^{n-2}+{\beta }^{n-3}+\cdots +\beta +1.$$ In this paper we define the shrinking random $\beta$-tran…