Normality preserving operations for Cantor series expansions and\n associated fractals part II

2014/07/03 by Dylan Airey, Airey, Dylan, Bill Mance +3 · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1407.0778

Abstract

We investigate how non-zero rational multiplication and rational addition\naffect normality with respect to Q-Cantor series expansions. In particular,\nwe show that there exists a Q such that the set of real numbers which are\nQ-normal but not Q-distribution normal, and which still have this property\nwhen multiplied and added by rational numbers has full Hausdorff dimension.\nMoreover, we give such a number that is explicit in the sense that it is\ncomputable.\n

Citations

• Subsequences of normal sequences

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• Cantor series expansions and packing dimension faithfulness

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