Ratio ergodic theorems for maps with indifferent fixed points
Ratio ergodic theorems for maps with indifferent fixed points
复制标题
具有无关不动点的映射的比率遍历定理
DOI：
10.1017/s0143385797084952
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发表时间：
1997
影响因子：
0.9
通讯作者：
Tomoki Inoue
中科院分区：
文献类型：
--
作者：
Tomoki Inoue
我们研究具有无差异不动点$p$和$q$的一维变换$T$（$p$和$q$是不动点$T^{\prime}(p) = T^{\prime}(q) = 1 $）。在$T$具有勒贝格等效无限不变测度的情况下，我们给出了比值遍历定理，该定理描述了轨迹$\{T^k(x)\}_{k=0}^n$在$p$小邻域中的停留时间与$q$小邻域中轨迹$\{T^k(x)\}_{k=0}^n$的停留时间之比的极限值。
We study one-dimensional transformations $T$ with indifferent fixed points $p$ and $q$ ($p$ and $q$ are fixed points with $ T^{\prime}(p) = T^{\prime}(q) = 1 $). In the case when $T$ has a Lebesgue equivalent infinite invariant measure, we give the ratio ergodic theorems which describe the limit value of the ratio of the sojourn time of the trajectory $\{T^k(x)\}_{k=0}^n$ in a small neighborhood of $p$ to that in a small neighborhood of $q$.