I will present two results joint with Lingmin Liao. The first is calculation of Hausdorff dimension of the multiplicative golden shift and related multiplicative multifractal sets in the setting when the maps are linear but not with a constant slope. The second is solving a question about inhomogeneous Diophantine approximations: how big is the set of points belonging to infinitely many balls of form B(nα,r_n) depending on the Diophantine type of α. This strengthens results of Bugeaud, Troubetskoy&Schmelling, and Xu.