循环上迭代函数系的稳定性
Stability of iterated function systems on the circle
摘要：
证明了任何至少有一个环同胚具有稠密轨道的迭代函数系是渐近稳定的。证明了相应的Perron-Frobenius算子满足e-性质，即对任何连续函数，其迭代都是等度连续的.证明了这类函数系从任意点出发的轨迹的强大数律。
英文摘要：
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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