Sojourn times in small neighborhoods of indifferent fixed points of one-dimensional dynamical systems
Sojourn times in small neighborhoods of indifferent fixed points of one-dimensional dynamical systems
复制标题
一维动力系统无差异不动点小邻域中的停留时间
DOI：
10.1017/s0143385700000110
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发表时间：
2000
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
我们研究了具有中立不动点p和q的一维动力系统。本文研究的动力系统具有遍历、无穷、不变测度。我们考虑了轨迹在p$的小邻域中的逗留时间与在q$的小邻域中的逗留时间之比的极限。我们证明了极限在某些条件下不存在，这在以前的论文中已经宣布。事实上，我们证明了该比率的极限上限是$\infty$，极限下确界是0。
We study one-dimensional dynamical systems with indifferent fixed points $p$ and $q$. The dynamical systems we study in this paper have ergodic, infinite, invariant measures. We consider the limit of the ratio of the sojourn time of the trajectory in a small neighborhood of $p$ to that in a small neighborhood of $q$. We show that the limit does not exist under some conditions, which has been announced in a previous paper. In fact we prove that the limit supreme of the ratio is $\infty$ and that the limit infimum is 0.