Corpus ID: 237503443

Dynamically defined subsets of generic self-affine sets

  title={Dynamically defined subsets of generic self-affine sets},
  author={Bal{\'a}zs B{\'a}r{\'a}ny and Sascha Troscheit},
In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article 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. These mild assumptions… Expand


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