The orbit of a ${\hat{I}}^2$-transformation cannot lie in a small interval

DoYong Kwon

For ${\hat{I}}^2>1$, let $T_{\hat{I}}^2:[0,1]\to [0,1)$ be the ${\hat{I}}^2$-transformation. We consider an invariant $T_{\hat{I}}^2$-orbit closure contained in a closed interval with diameter $1/{\hat{I}}^2$, then de…