Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions

Lior Fishman; Bill Mance; David Simmons; Mariusz Urbanski

Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions

Dynamical Systems 2015-09-08 v2 Number Theory

Authors: Lior Fishman , Bill Mance , David Simmons , Mariusz Urbanski

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 $\mathbb{R}/\mathbb{Z}$ , 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.

Keywords

shrinking target scheme non-autonomous dynamical systems Cantor series expansions Hausdorff dimension Bowen type formula Diophantine approximation

Cite

@article{arxiv.1409.7950,
  title  = {Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions},
  author = {Lior Fishman and Bill Mance and David Simmons and Mariusz Urbanski},
  journal= {arXiv preprint arXiv:1409.7950},
  year   = {2015}
}

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6 pages

Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions

Abstract

Keywords

Cite

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