Negative ${\hat{I}}^2$-transformations: invariant measures, subshifts of finite type and matching property

Yan Huang, Yun Sun

We study the negative beta transformations $T_{-{\hat{I}}^2}:=-{\hat{I}}^{2}x+\lfloor {\hat{I}}^{2}x\rfloor +1$ for $x\in (0,1]$ and ${\hat{I}}^2>1$. We present a complete characterization of pairs of dstinct non-integers…