Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions
Abstract
We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the non-autonomous dynamical system on the interval [0,1), viewed as R/Z, corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilizing our theorem. In particular, we provide a Diophantine approximation interpretation of our scheme.
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