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Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions
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| Journal | Bulletin of the Australian Mathematical Society |
|---|---|
| Date | E-pub ahead of print - 2 Jun 2015 |
| Date | Published (current) - Oct 2015 |
| Issue number | 2 |
| Volume | 92 |
| Pages (from-to) | 205-213 |
| Early online date | 2/06/15 |
| Original language | English |
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.
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© 2015 Australian Mathematical Publishing Association Inc. This is an author produced version of a paper accepted for publication in Bulletin of the Australian Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.
- math.DS, math.NT
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