局部最小通量曲面
Surfaces of locally minimal flux
摘要：
对于精确的保面积扭曲映射，通过\cite{MMP84}中的cantori间隙构造曲线，并保证曲线通过cantori点时具有最小通量. \cite{Pol}指出，如果同时存在一个具有不同旋转数的旋转不变圆，则这些曲线{ \em not}具有最小通量，但如果是双曲曲线，则即使没有通过Cantorus点的约束，它们也具有{ \em局部}最小通量。根据三维保体积流局部极小通量曲面的\cite{M94}准则，本文重新讨论了这一结果，并证明了一般情况下，通过旋转有序周期轨道或其异宿轨道上的点的类似曲线{ \em不}具有局部极小通量.一路上，各种各样的问题被提出。更多的自由度的一些结果进行了总结。
英文摘要：
For exact area-preserving twist maps, curves were constructed through the gaps of cantori in \cite{MMP84}, which were conjectured to have minimal flux subject to passing through the points of the cantorus. It was pointed out by \cite{Pol} that these curves do {\em not} have minimal flux if there coexists a rotational invariant circle of a different rotation number, but if hyperbolic they do have {\em locally} minimal flux even without the constraint of passing through the points of the cantorus. Following the criterion of \cite{M94} for surfaces of locally minimal flux for 3D volume-preserving flows, I revisit this result and show that in general the analogous curves through the points of rotationally-ordered periodic orbits or their heteroclinic orbits do {\em not} have locally minimal flux. Along the way, various questions are posed. Some results for more degrees of freedom are summarised.
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