ИСТИНА

The Minkowski question-mark function ?(x) is a continuous and strictly increasing function, which maps the [0, 1] interval onto itself. Given the explicit formula for ?(x), one can see that the equation ?(x) = x has at least 5 solutions, a folklore conjecture states that there are exactly 5 fixed points of ?(x). We will tell about some new results on Diophantine properties of fixed points of ?(x). We also give a condition from which the conjecture about the fixed points would follow. The talk is based on a joint work with Dmitry Gayfulin.