具有非零通量的保体积映射中的输运和混合障碍
Barriers to Transport and Mixing in Volume-Preserving Maps with Nonzero Flux
摘要：
在本文中，我们确定的几何结构，限制运输和混合扰动的可积保体积系统与非零净流量。与KAM环面不同，这些物体不能延续到可积系统中存在的环面，而是由共振产生的，并且具有可收缩的方向。我们引入了一个非常简单的算法来分析这些地图的行为，并获得定量性质的环面。特别是，我们提出的断言关于逃逸时间的无界轨道，丰富的环面的分布，和共振区域的大小。
英文摘要：
In this paper we identify the geometric structures that restrict transport and mixing in perturbations of integrable volume-preserving systems with nonzero net flux. Unlike KAM tori, these objects cannot be continued to the tori present in the integrable system but are generated by resonance and have a contractible direction. We introduce a remarkably simple algorithm to analyze the behavior of these maps and obtain quantitative properties of the tori. In particular, we present assertions regarding the distribution of the escape times of the unbounded orbits, the abundance of tori, and the size of the resonant regions.
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