A fractal perturbation technique yields the dimensions of integral self-affine sets and proves existence of full-dimensional ergodic measures on their torus versions.
Seneta, Non-negative Matrices and Markov Chains, 2nd Edition, Springer-Verlag
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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.