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arXiv · 1702.05356

Stability of iterated function systems on the circle

Tomasz Szarek·Anna Zdunik
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Abstract

We prove that any Iterated Function System of circle homeomorphisms with at least one of them having dense orbit, is asymptotically stable. The corresponding Perron-Frobenius operator is shown to satisfy the e-property, that is, for any continuous function its iterates are equicontinuous. The Strong Law of Large Numbers for trajectories starting from an arbitrary point for such function systems is also proved.

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Tomasz Szarek, Anna Zdunik. 2017-02-17. Stability of iterated function systems on the circle. https://arxiv.org/abs/1702.05356

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