Kurzweil type metrical Diophantine properties in the field of formal Laurent series

In this article, we consider Diophantine properties of the orbit of irrational rotations over the field of formal Laurent series F q ( ( X − 1 ) ) . More precisely, for a given f ∈ F q ( ( X − 1 ) ) and a sequence ( r n ) , we investigate the size of the set { g ∈ F q ( ( X − 1 ) ) : min deg Q = n | { Q f } − g | < r n  for infinitely many n ∈ N } in the sense of the Haar measure and the Hausdorff dimension.