Normal and Non‐Normal Points of Self‐Similar Sets and Divergence Points of Self‐Similar Measures

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A PANORAMA OF SPECIFICATION-LIKE PROPERTIES AND THEIR CONSEQUENCES (2015, background): “There is a vast literature on this topic, see [63, 62, 29] to mention only a few contributions.”
Topological and fractal properties of real numbers which are not normal (2005, unknown): “Let us consider two sequencesk ′ m(i) = k ′ m andk ′′ m(i) = k ′′ m,m∈ N, wherek ′ m+ 1 is the number of the position at which the m-th group of the fixed digits ”i” is started, andk ′′ m is the number of the position at which the m-th group of the fixed digits ”i” is finished.”
Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices (2003, background): “Theorem A extends the corresponding results for the Birkho averages of scalar functions, for which one is referred to, e.g., [1, 2, 3, 9, 10, 16, 35, 38 , 40, 41, 47].”
Divergence points of self-similar measures and packing dimension (2007, methodology): “Indeed, in [20,21] we computed the Hausdorff dimension of this set, see Theorem C below.”