论文标题
计算分段线性系统中的lyapunov弯曲
Counting the Lyapunov inflections in piecewise linear systems
论文作者
论文摘要
在Iommi-Kiwi和Jenkinson-Pollicott-vytnova的开创性工作之后，我们继续研究这项工作中Lyapunov Spectrum的拐点。我们证明，对于任何3个分支分段线性的线性扩展地图，其Lyapunov拐点的数量上方限制为2。这些结果给出了Jenkinson-Pollicott-vytnova问题的答案，以观察到分段线性图的Lyapunov频谱中4个弯曲所需的分支数量最少。在一般情况下，我们对任何N分支分段线性扩展地图的Lyapunov拐点数量给出了上限，并构建了一个N-Branch分段线性膨胀图的家族，并具有2N-4 Lyapunov函数。我们还考虑了这项工作中基本分支编号的单词分段线性地图的lyapunov数量。在工作的情况下，在整个工作中，分段线性图的分布有一些结果。
Following the pioneering work of Iommi-Kiwi and Jenkinson-Pollicott-Vytnova, we continue to study the inflection points of the Lyapunov spectrum in this work. We prove that for any 3-branch piecewise linear expanding map on an interval, the number of its Lyapunov inflections is bounded above by 2. Then we continue to show that, there is a 4-branch piecewise linear expanding map, such that its Lyapunov spectrum has exactly 4 inflection points. These results give an answer to a question by Jenkinson-Pollicott-Vytnova on the least number of branches needed to observe 4 inflections in the Lyapunov spectrum of piecewise linear maps. In the general case, we give upper bound on the number of Lyapunov inflections for any n-branch piecewise linear expanding maps, and construct a family of n-branch piecewise linear expanding maps with 2n-4 Lyapunov inflections. We also consider the number of Lyapunov inflections of piecewise linear maps in words of the essential branch number in this work. There are some results on distributions of the Lyapunov inflections of piecewise linear maps through out the work, in case of their existence.
