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arXiv · 1211.3647

Diophantine property in the group of affine transformations of the line

Péter Pál Varjú
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Abstract

We investigate the Diophantine property of a pair of elements in the group of affine transformations of the line. We say that a pair of elements g_1,g_2 in this group is Diophantine if there is a number A such that a product of length l of elements of the set {g_1,g_2,g_1^{-1},g_2^{-1}} is either the unit element or of distance at least A^{-l} from the unit element. We prove that the set of non-Diophantine pairs in a certain one parameter family is of Hausdorff dimension 0.

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Péter Pál Varjú. 2013-07-12. Diophantine property in the group of affine transformations of the line. https://doi.org/10.14232/actasm-013-757-6

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