Falconer, Kenneth; Sloan, Arron Continuity of subadditive pressure for self-affine sets. (English) Zbl 1196.37046 Real Anal. Exch. 34(2008-2009), No. 2, 413-427 (2009). 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. Reviewer: Nicolae-Adrian Secelean (Sibiu) Cited in 1 ReviewCited in 19 Documents MSC: 37C45 Dimension theory of smooth dynamical systems 28A78 Hausdorff and packing measures Keywords:pressure; subadditive; submultiplicative; fractal; self-affine PDFBibTeX XMLCite \textit{K. Falconer} and \textit{A. Sloan}, Real Anal. Exch. 34, No. 2, 413--427 (2009; Zbl 1196.37046) Full Text: DOI Link