Sala Conferenze (Puteano, Centro De Giorgi).
We investigate how the dynamics of a countable Markov map change when the map is perturbed by analysing the topological conjugacy maps between the original and perturbed system. These conjugacies are strictly increasing singular maps (i.e., with derivative Lebesgue-almost-everywhere equal to zero). We can show that under certain conditions, the Hausdorff dimension of the set of points where the derivative is nonzero is continuous, in the sense that as the perturbation is made smaller and smaller, the dimension tends to 1. On the other hand, for various other quantities (including Hoelder exponent) we give simple examples to show discontinuity in the conjugacy maps.