Ergodic invariant measures of order preserving random dynamical systems on the real line are Dirac measures
Dynamical Systems
2026-02-18 v1 Probability
Abstract
It is well known that ergodic invariant measures for order preserving two-sided time random dynamical systems(RDS) on the real line are Dirac. In the present note this is shown to hold also for one-sided time RDS.
Keywords
Cite
@article{arxiv.2602.15144,
title = {Ergodic invariant measures of order preserving random dynamical systems on the real line are Dirac measures},
author = {Hans Crauel},
journal= {arXiv preprint arXiv:2602.15144},
year = {2026}
}