Iterated function systems with super-exponentially close cylinders (Q2220470)

It is known that, if the Hausdorff dimension of a self-similar measure in \(\mathbb{R}\) does not equal its expected value, then there are cylinders which are super-exponentially close at all small scales. Moreover, a similar statement holds for the \(L^q\) dimension of self-similar measures in \(\mathbb{R}\). With these statements in mind, the author proves the existence of iterated function systems that do not contain exact overlaps, yet there are cylinders which are super-exponentially close at all small scales.