For a circle map $f\colon\mathbb{ S}\to\mathbb{ S}$ with zero topological entropy, we show that a non-diagonal pair $\langle x,y\rangle\in \mathbb{ S}\times \mathbb{ S}$ is non-separable if and only if it is an IN-pair if and only if it is an IT-pair. We also show that if a circle map is topological null then the maximal pattern entropy of every open cover is of polynomial order.
Categories: math.DS