English

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 R\mathbb R 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}
}