Towards Absolutely Continuous Bernoulli Convolutions

Abstract

We show how to turn the question of the absolute continuity of Bernoulli convolutions into one of counting the growth of the number of overlaps in the system. When the contraction parameter is a hyperbolic algebraic integer, we turn this question of absolute continuity into a question involving the ergodic theory of cocycles over domain exchange transformations.

References in corpus (6)

• On self-similar sets with overlaps and inverse theorems for entropy
• Absolute continuity of Bernoulli convolutions for algebraic parameters
• Absolute Continuity of Self Similar Measures
• Estimates on the dimension of self-similar measures with overlaps
• Measures on the Spectra of Algebraic Integers
• Self-similar sets and measures on the line