A note on the points with dense orbit under the expansions of different bases

Wen-Ya Wang

Chaos, Solitons & Fractals, 2015, vol. 77, issue C, 235-239

Abstract: It was conjectured by Furstenberg that for any x∈[0,1]∖Q,dimH{2nx(mod1):n≥1}¯+dimH{3nx(mod1):n≥1}¯≥1,where dimH denotes the Hausdorff dimension and A¯ denotes the closure of a set A. When x is a normal number, the above result holds trivially. In this note, we are aiming at giving explicit non-normal numbers for which the above dimensional formula holds.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:77:y:2015:i:c:p:235-239

DOI: 10.1016/j.chaos.2015.06.003

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