## Hausdorff dimension of the multiplicative golden mean shift

*Kenyon, Richard*;

*Peres, Yuval*;

*Solomyak, Boris*;

- Subject: 37C45 (Primary), 28A78, 37D35 (Secondary) | Mathematics - Dynamical Systems | Mathematics - Number Theory

We compute the Hausdorff dimension of the "multiplicative golden mean shift" defined as the set of all reals in $[0,1]$ whose binary expansion $(x_k)$ satisfies $x_k x_{2k}=0$ for all $k\ge 1$, and show that it is smaller than the Minkowski dimension.

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UNIVERSITY OF WASHINGTON 90%UNIVERSITY OF WASHINGTON (PREVIOUSLY U OF CHICAGO 90PD0276) 90%BROWN UNIVERSITY 90%Microsoft Research (India) ( Microsoft Research (India) ) IndiaWebsite url: http://research.microsoft.com/en-us/labs/india/90%UNIVERSITY OF WASHINGTON - 1 88%Brown University ( Brown University ) United StatesWebsite url: http://www.brown.edu/90%Microsoft Research (Germany) ( MSR ) Germany90%University of Washington ( UW ) United StatesWebsite url: http://www.washington.edu/90%University Of Washington 90%UNIVERSITY OF WASHINGTON: 90% - Metrics

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