Hausdorff Dimension of Some Groups Acting on the Binary Tree
نویسنده
چکیده
Based on the work of Abercrombie [1], Barnea and Shalev [3] gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T . Abért and Virág [2] showed that there exist finitely generated (but not necessarily level-transitive) subgroups of AutT of arbitrary dimension in [0, 1]. We give the first deterministic construction of finitely generated groups of irrational Hausdorff dimension. More precisely, we show that the set of Hausdorff dimensions of the 3-generated level-transitive spinal groups contains a Cantor set which contains transcendental elements.
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