分界线混沌层的最大宽度
Maximal width of the separatrix chaotic layer
摘要：
本文的主要目的是寻找具有分界线的一维Hamilton系统的分界线混沌层宽度的{ \it绝对最大值}作为时间周期扰动频率的函数，这是分界线混沌理论中尚未解决的主要问题之一.对于一个给定的小振幅的扰动，宽度示出具有尖锐的峰值范围内从temperamically小到中等频率。这些峰值是普遍的，是非线性共振动力学参与分界线混沌运动的结果。进一步发展Soskin等人在最近的论文（{ \it PRE} { \bf 77}，036221（2008））中介绍的方法，我们导出低频峰形状的领先阶渐近表达式。峰值的最大值，特别包括宽度的{ \it绝对最大值}，与扰动幅度乘以数值上大的因子或数值上的（通常仍然是大的）因子成比例，这取决于系统的类型。因此，我们的理论预测，混沌层的最大宽度可能比以前的理论预测的大得多。理论在仿真中得到了验证。应用程序的促进全球混沌发病进行了讨论。
英文摘要：
The main goal of the paper is to find the {\it absolute maximum} of the width of the separatrix chaotic layer as function of the frequency of the time-periodic perturbation of a one-dimensional Hamiltonian system possessing a separatrix, which is one of the major unsolved problems in the theory of separatrix chaos. For a given small amplitude of the perturbation, the width is shown to possess sharp peaks in the range from logarithmically small to moderate frequencies. These peaks are universal, being the consequence of the involvement of the nonlinear resonance dynamics into the separatrix chaotic motion. Developing further the approach introduced in the recent paper by Soskin et al. ({\it PRE} {\bf 77}, 036221 (2008)), we derive leading-order asymptotic expressions for the shape of the low-frequency peaks. The maxima of the peaks, including in particular the {\it absolute maximum} of the width, are proportional to the perturbation amplitude times either a logarithmically large factor or a numerical, still typically large, factor, depending on the type of system. Thus, our theory predicts that the maximal width of the chaotic layer may be much larger than that predicted by former theories. The theory is verified in simulations. An application to the facilitation of global chaos onset is discussed.
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