Hausdorff dimension of the limit sets of some planar geometric constructions

By Krzysztof Barański. 2007

138 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f42955d0050d71958bd95588c23f1b637352ea9a

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In Mathematical Physics

Citations in the corpus

Assouad Dimension and Fractal Geometry (2020, background): “This strategy led to various different classes of selfaffine carpet being introduced with increasing levels of generality, see [122, 15, 83, 86, 172, 168, 102].”
Dimension theory of iterated function systems (2009, methodology): “References [1] Barański, K. Hausdorff dimension of the limit sets of some planar geometric constructions.”
Ledrappier-Young formula and exact dimensionality of self-affine measures (2015, background): “Bárány also acknowledges the support from the grants EP/J013560/1 and OTKA K104745 and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. where ‖v‖ denotes the Euclidean norm of a vector v.”
Assouad dimension of self-affine carpets (2010, methodology): “After the work of Bedford and McMullen, the Hausdorff and upper Minkowski dimension of more general sets were studied by Lalley and Gatzouras [9], Barański [2] and others.”
Dimension of invariant measures for affine iterated function systems (2019, result): “Later, Gatzouras and Lalley [35] and Barański [1] obtained similar results for a class of more general carpet-like self-affine sets in the plane.”
Hausdorff dimension of planar self-affine sets and measures (2017, background): “All these results provide strong evidence that the a nity dimension is typically the right one, but one should note that the dimension is not always equal to the a nity dimension, as demonstrated by carpet-like fractals [32, 6, 29, 2, 16].”