Abstract:
Bernoulli Convolutions are a well known family of self-similar measures with overlaps. The question of whether or not the Bernoulli convolution associated to some particular parameter is absolutely continuous goes back to work of Erdos in the 1930s. We look at parameters beta in (1,2) which are algebraic and for which none of the Galois conjugates have absolute value equal to 1, in this case we are able to turn the question of the absolute continuity of the Bernoulli convolution into a question involving cut and project sets and the ergodic theory of cocyles over domain exchange transformations. This is joint work with Alex Batsis.