Circularly invariant uniformizable probability measures for linear transformations
Dynamical Systems
2017-06-09 v4 Probability
Abstract
In this paper, we prove a threshold result on the existence of a circularly invariant uniformizable probability measure (CIUPM) for linear transformations with non-zero slope on the line. We show that there is a threshold constant depending only on the slope of the linear transformation such that there exists a CIUPM if and only if its support has a diameter at least as large as Moreover, the CIUPM is unique up to translation if the diameter of the support equals
Keywords
Cite
@article{arxiv.1609.08204,
title = {Circularly invariant uniformizable probability measures for linear transformations},
author = {Chuang Xu},
journal= {arXiv preprint arXiv:1609.08204},
year = {2017}
}