Falconer's formula for the Hausdorff dimension of a self-affine set in R² (with S.P. Lalley) Ergodic Theory and Dynamical Systems, 15, 77-97 (1995)

Simple sufficient conditions are given for the validity of a formula of Falconer (1988) describing the Hausdorff dimension (and Minkowski dimension) of a self-affine set. These conditions are natural (and easily checked) geometric restrictions on the actions of the affine mappings determining the self-affine set. It is also shown that under these hypotheses the self-affine set supports an invariant Gibbs measure whose Hausdorff dimension equals that of the set.