Recurrence to shrinking targets on typical self-affine fractals

Abstract

We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a certain related symbolic recurrence set. In many cases this set is equivalent to the recurring set on the fractal.

arXiv comment16 pages; v2: main result has improved