Local complexity functions of interval exchange transformations

We studied numerically complexity functions for interval exchange transformations. We have shown that they grow linearly in time as well as the ϵ-complexity function. Moreover, we found out that they depend also linearly on ϵ where ϵ is the Lebesgue measure of a set of initial points. This allows us to hypothesize that the dimension of the measure related to the ϵ-complexity function could be determined by studying the dependence of local complexity functions on ϵ.