Continuity of subadditive pressure for matrix cocycles and the dimension of a self-affine set

Abstract

The pressure function P(A,s) and singularity dimension s(A) are closely related to the dimension of a typical self affine set. De-Jun Feng and Pablo Shmerkin proved in their article “Non-conformal repellers and continuity of pressure for matrix cocycles” that P(A,s) and s(A) depend continuously on the linear maps A. This is achieved by proving the continuity of a more general pressure for matrix cocycles. In this thesis we proof these continuity results following the arguments of Feng and Shmerkin. Compared to the original article the proofs are given with greater details and more necessary background is covered.