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Dynamics Lunch: Amir Algom "On \alpha \beta sets." | Einstein Institute of Mathematics

Dynamics Lunch: Amir Algom "On \alpha \beta sets."

Date: 
Tue, 23/10/201812:00-13:00
Location: 
Manchester faculty club

Let $\alpha, \beta$ be elements of infinite order in the circle group. A closed set K in the circle is called an \alpha \beta set if for every x\in K either x+\alpha \in K or x+\beta \in K. In 1979 Katznelson proved that there exist non-dense \alpha \beta sets, and that there exist \alpha \beta sets of arbitrarily small Hausdorff dimension. We shall discuss this result, and a more recent result of Feng and Xiong, showing that the lower box dimension of every \alpha \beta set is at least 1/2. We shall also explain how the study of \alpha \beta sets is related to some modern problems in fractal geometry.