Shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. We introduce a mild condition on the linear parts of the affine mappings that allow us to bound the Hausdorff dimension of cylindrical shrinking target and recurrence sets. For generic self-affine sets in the sense of Falconer, that is by randomising the translation part of the affine maps, we prove that these bounds are sharp. We will put our mild assumption in historical context to show how our results extend and complement the existing literature for recurrence on self-affine sets.
(Joint with Balázs Bárány)