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Continuity of subadditive pressure for self-affine sets. (English) Zbl 1196.37046

A “pressure” functional \(\Phi^s(T_1,\dots,T_N)\), defined as the limit of sums of singular value functions of products of linear mappings \((T_1,\dots,T_N)\), is central in analyzing fractal dimensions of self-affine sets. The authors proves that, in some properly conditions, \(\Phi^s\) is continuous with respect to the linear mappings \((T_1,\dots,T_N)\) which underlie the self-affine sets (Theorems 2.5, 3.3, Proposition 4.2). The paper is very well written and the subject is of large interest.

MSC:

37C45 Dimension theory of smooth dynamical systems
28A78 Hausdorff and packing measures
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