A fractal perturbation technique yields the dimensions of integral self-affine sets and proves existence of full-dimensional ergodic measures on their torus versions.
Billingsley, Convergence of Probability Measures, 2nd ed., John Wiley & Sons, Inc., New York, 1999
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The Dimension of Integral Self-Affine Sets via Fractal Perturbations: The Box and the Hausdorff Dimensions, Ergodic Measures
A fractal perturbation technique yields the dimensions of integral self-affine sets and proves existence of full-dimensional ergodic measures on their torus versions.