Hausdorff dimension of self-affine limit sets with an invariant direction
Consider the self-affine limit sets for some classes of iterated function systems in the plane with invariant direction, such as a generalized Sierpiński gasket. The main result in this short paper determines the Hausdorff dimension and the box dimension of such objects. The outcome is further illustrated by a number of examples and figures. This paper extends earlier results of \textit{S. P. Lalley} and \textit{D. Gatzouras} [Indiana Univ. Math. J. 41, No. 2, 533--568 (1992; Zbl 0757.28011)] and contributes to some problems mentioned in [\textit{K. J. Falconer, B. Lammering}, Fractals 6, No.1, 31--41 (1998; Zbl 1012.28012)]. The arguments are essentially based on [\textit{K. Barański}, Adv. Math. 210, No. 1, 215--245 (2007; Zbl 1116.28008)].
scientific article; zbMATH DE number 5315188