Singularity results for functional equations driven by linear fractional transformations
Probability
2015-11-30 v2 Classical Analysis and ODEs
Abstract
We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.
Cite
@article{arxiv.1205.3632,
title = {Singularity results for functional equations driven by linear fractional transformations},
author = {Kazuki Okamura},
journal= {arXiv preprint arXiv:1205.3632},
year = {2015}
}
Comments
14 pages, Title changed, to appear in Journal of Theoretical Probability