S-unimodal Misiurewicz maps with flat critical points
S-unimodal Misiurewicz maps with flat critical points
复制标题
具有平坦临界点的 S-单峰 Misiurewicz 映射
DOI：
10.4064/fm181-1-1
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发表时间：
2004
影响因子：
0.6
通讯作者：
Roland Zweimüller
中科院分区：
文献类型：
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作者：
Roland Zweimüller
我们考虑S-单峰Misiurewicz映射T与平坦的临界点c，并表明它们表现出遍历性质类似的区间映射的中立不动点（或周期）。具体地说，存在一个保守的遍历绝对连续的σ-有限不变测度μ，精确到有限旋转，并且在无限测度的情况下，系统是具有许多一致集和Darling-Kac集的点态对偶遍历。确定适当的参考集的回报分布的顺序，我们得到的衰减的相关性和游荡率的界限。假设一些控制的局部行为T在C，我们表明，在大多数情况下，例如，每当过临界轨道有一个李雅普诺夫指数，尾部的回报分布实际上是经常变化的，这意味着精确的信息的混合率，和各种分布极限定理。AMS科目分类：28 D 05、37 A25、37 A40、37 E05、60 F05
We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable reference sets we obtain bounds on the decay of correlations and on wandering rates. Assuming some control of the local behaviour of T at c, we show that in most cases, e.g. whenever the postcritical orbit has a Lyapunov exponent, the tail of the return distribution is in fact regularly varying, which implies precise information on the mixing rate, and various distributional limit theorems. AMS subject classification: 28D05, 37A25, 37A40, 37E05, 60F05