English

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.

Keywords

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

R2 v1 2026-06-21T21:04:57.425Z