小随机扰动下的Sharkovski定理
Sharkovskiis theorem under small random perturbations
AI总结：
本文通过随机Conley指数，建立了小随机扰动下的一维映射随机动力系统的Sharkovskii型定理，实现了对随机周期点的精确检测。
摘要：
我们通过随机Conley指数，为一类离散随机动力系统建立了Sharkovskii型定理。利用Conley指数的延续性性质，我们将经典forcing结果扩展到由小随机扰动的一维映射得到的随机系统中。与以往测度论结果不同，后者通常面临固有的周期翻倍模糊性（实现周期n或2n），我们的拓扑方法允许我们精确检测随机周期点和轨道的最小周期。这产生了Sharkovskii序任意有限尾的实现结果。这些结果通过构造扰动后的帐篷映射和Logistic映射的随机周期轨道来说明。
英文摘要：
We establish a Sharkovskii-type theorem for a class of discrete random dynamical systems via the random Conley index. Using the continuation property of the Conley index, we extend classical forcing results to random systems obtained from small random perturbations of one-dimensional maps. In contrast to earlier measure-theoretic results, which are typically subject to an inherent period-doubling ambiguity (realizing period $n$ or $2n$), our topological approach allows us to detect random periodic points and orbits with precise minimal periods. This yields realisation results for arbitrary finite tails of the Sharkovskii ordering. These results are illustrated by constructing random periodic orbits for perturbed versions of the tent map and the logistic map.
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