English

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 cc 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 c.c. Moreover, the CIUPM is unique up to translation if the diameter of the support equals c.c.

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}
}
R2 v1 2026-06-22T16:02:09.597Z