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

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JournalBulletin of the Australian Mathematical Society
DateE-pub ahead of print - 2 Jun 2015
DatePublished (current) - Oct 2015
Issue number2
Volume92
Pages (from-to)205-213
Early online date2/06/15
Original languageEnglish

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.

    Research areas

  • math.DS, math.NT

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