Geometric and Symbolic Local Dimensions of Continued Fractions

We are interested in calculating upper and lower geometric local dimensions of continued fractions, with respect to the equilibrium measure. It is often difficult to calculate geometric local dimensions. It is much easier to calculate upper and lower symbolic local dimensions. It is believed that the geometric local dimension at a continued fraction x exists if and only if symbolic local dimension exists at x, and what is more, they coincide for almost all points. In my talk I will establish a relationship between these two types of dimensions.