Motivated by the long-standing problem of finding sharp lower estimates for the Hausdorff dimension of self-affine sets, I will describe some recent results on the equilibrium states of the singular value function. These equilibrium states arise as candidates for the measures of maximal Hausdorff dimension on self-affine sets. In particular I will discuss a sufficient condition for uniqueness of the equilibrium state (from joint work with Antti Käenmäki) and an unconditional bound for the number of ergodic equilibrium states (from joint work with Jairo Bochi).
Tue, 16/05/2017 (All day)
Equilibrium states of affine iterated function systems