Normality preserving operations for Cantor series expansions and associated fractals part I

Dylan Airey; Bill Mance

Normality preserving operations for Cantor series expansions and associated fractals part I

Number Theory 2014-07-10 v2

Authors: Dylan Airey , Bill Mance

Abstract

It is well known that rational multiplication preserves normality in base $b$ . We study related normality preserving operations for the $Q$ -Cantor series expansions. In particular, we show that while integer multiplication preserves $Q$ -distribution normality, it fails to preserve $Q$ -normality in a particularly strong manner. We also show that $Q$ -distribution normality is not preserved by non-integer rational multiplication on a set of zero measure and full Hausdorff dimension.

Keywords

normality preserving operations Cantor series expansions $Q$-normality $Q$-distribution normality rational multiplication Hausdorff dimension fractals

Cite

@article{arxiv.1407.0777,
  title  = {Normality preserving operations for Cantor series expansions and associated fractals part I},
  author = {Dylan Airey and Bill Mance},
  journal= {arXiv preprint arXiv:1407.0777},
  year   = {2014}
}

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10 pages

Normality preserving operations for Cantor series expansions and associated fractals part I

Abstract

Keywords

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