Abstract
We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (xk) satisfies xkx2k=0 for all k≥1, and show that it is smaller than the Minkowski dimension. 2011 Académie des sciences.
Translated title of the contribution | Hausdorff dimension of the multiplicative golden mean shift |
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Original language | French |
Pages (from-to) | 625-628 |
Number of pages | 4 |
Journal | Comptes Rendus Mathematique |
Volume | 349 |
Issue number | 11-12 |
DOIs | |
State | Published - Jun 2011 |
Externally published | Yes |
Bibliographical note
Funding Information:We are grateful to Jörg Schmeling for telling us about the problem, and to Aihua Fan, Lingmin Liao, and Jihua Ma for sending us their preprint [4] prior to publication. The research of R.K. and B.S. was supported in part by NSF.
Funding
We are grateful to Jörg Schmeling for telling us about the problem, and to Aihua Fan, Lingmin Liao, and Jihua Ma for sending us their preprint [4] prior to publication. The research of R.K. and B.S. was supported in part by NSF.
Funders | Funder number |
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National Science Foundation | 0968879 |