Towards Absolutely Continuous Bernoulli Convolutions
Dynamical Systems
2021-10-19 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2110.09072,
title = {Towards Absolutely Continuous Bernoulli Convolutions},
author = {Alex Batsis and Tom Kempton},
journal= {arXiv preprint arXiv:2110.09072},
year = {2021}
}