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arXiv · 2602.15144

Ergodic invariant measures of order preserving random dynamical systems on the real line are Dirac measures

Hans Crauel
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Abstract

It is well known that ergodic invariant measures for order preserving two-sided time random dynamical systems(RDS) on the real line $\mathbb R$ are Dirac. In the present note this is shown to hold also for one-sided time RDS.

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Hans Crauel. 2026-02-16. Ergodic invariant measures of order preserving random dynamical systems on the real line are Dirac measures. https://arxiv.org/abs/2602.15144

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