Singular potentials, rigidity and recurrence in low dimensional dynamics
In the first part of this thesis we study the behaviour of the equilibrium measure and the Birkhoff sums for a singular potential over the doubling map. A complete multifractal analysis for the the Birkhoff sums and the equilibrium measure (for the ’appropriate’ scaling) is given in Paper I. In Paper II we prove a parameter continuity property of the pressure function for a family of singular pote