Diophantine property in the group of affine transformations of the line
  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. 
P\'eter P\'al Varj\'u
math.GR math.CA math.NT