Abstract
In an earlier work, joint with R. Kenyon, we computed the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in [0,1] whose binary expansion (xκ) satisfies xκx2κ = 0 for all κ ≥ 1. Here we show that this set has infinite Hausdorff measure in its dimension. A more precise result in terms of gauges in which the Hausdorff measure is infinite is also obtained.
| Original language | English |
|---|---|
| Title of host publication | Further Developments in Fractals and Related Fields |
| Editors | Julien Barral, Stéphane Seuret |
| Publisher | Springer International Publishing |
| Pages | 193-212 |
| Number of pages | 20 |
| ISBN (Print) | 9780817683993 |
| DOIs | |
| State | Published - 2013 |
| Externally published | Yes |
| Event | International Conference on Fractals and Related Fields, 2011 - Porquerolles Island, France Duration: 1 Jun 2011 → … |
Publication series
| Name | Trends in Mathematics |
|---|---|
| Volume | 55 |
| ISSN (Print) | 2297-0215 |
| ISSN (Electronic) | 2297-024X |
Conference
| Conference | International Conference on Fractals and Related Fields, 2011 |
|---|---|
| Country/Territory | France |
| City | Porquerolles Island |
| Period | 1/06/11 → … |
Bibliographical note
Publisher Copyright:© Springer Science+Business Media New York 2013.
Funding
The research of B. S. was supported in part by the NSF grant DMS-0968879. He is grateful to the Microsoft Research Theory Group for hospitality during 2010–2011. He would also like to thank the organizers of the conference “Fractals and Related Fields II” for the excellent meeting and stimulating atmosphere. The authors are grateful to the referee for careful reading of the manuscript and many helpful comments.
| Funders | Funder number |
|---|---|
| National Science Foundation | DMS-0968879 |
| Directorate for Mathematical and Physical Sciences | 0968879 |