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The two-dimensional density of Bernoulli Convolutions

Bernoulli convolutions form a one-parameter family of self-similar measures on the unit interval. We suggest to study their two-dimensional density which has an intricate combinatorial structure. Visualizing this structure we discuss results of Erdös, Jóo, Komornik, Sidorov, de Vries, Jordan, Shmerkin and Solomyak, Feng and Wang. We emphasize the rôle of finite orbits of associated multivalued maps and mention a few new properties and examples.

preprint2016arXivOpen access
Christoph Bandt
math.DS
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Christoph Bandt

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