Local dimensions for the random beta-transformation
Dynamical Systems
2012-11-05 v1
Abstract
The random beta-transformation K is isomorphic to a full shift. This relation gives an invariant measure for K that yields the Bernoulli convolution by projection. We study the local dimension of the invariant measure for K for special values of beta and use the projection to obtain results on the local dimension of the Bernoulli convolution.
Cite
@article{arxiv.1211.0454,
title = {Local dimensions for the random beta-transformation},
author = {Karma Dajani and Charlene Kalle},
journal= {arXiv preprint arXiv:1211.0454},
year = {2012}
}
Comments
19 pages, 3 figures