Absolute Continuity of Self Similar Measures
Dynamical Systems
2023-02-07 v3 Classical Analysis and ODEs
Abstract
We prove that a self similar measure is absolutely continuous providing that it satisfies a condition depending on its Garsia entropy, contraction ratio, and the separation between different points in approximations of the self similar measure. In the special case of Bernoulli convolutions this paper gives a sufficient condition for the Bernoulli convolution with parameter lambda to be absolutely continuous in terms of lambda and its Mahler measure.
Cite
@article{arxiv.2103.12684,
title = {Absolute Continuity of Self Similar Measures},
author = {Samuel Kittle},
journal= {arXiv preprint arXiv:2103.12684},
year = {2023}
}
Comments
This version of the paper has been accepted by Annales scientifiques de l'\'Ecole normale sup\'erieure