基于双尺度Cantor测度的混沌吸引子参数刻画
Parametric characterisation of a chaotic attractor using two scale Cantor measure
摘要：
一个混沌吸引子的特征通常是它的多重分形谱，它给出了它的复杂性的几何度量。在这里，我们提出了一个使用最小的一组独立的参数，这是唯一确定的基本过程中产生的吸引子的特性。该方法将一个混沌吸引子的f（alpha）谱映射到一个一般的双尺度Cantor测度的f（alpha）谱上。我们表明，映射可以做大量的混沌系统。为了实现这一过程，我们还提出了一个推广的标准方程的两个尺度康托集在一维到更高的维度。另一个有趣的结果，我们已经得到了理论和数值是，f（alpha）的特性只给信息高达两个尺度，即使当底层的过程中产生的多重分形涉及两个以上的尺度。
英文摘要：
A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independant parameters which are uniquely determined by the underlying process that generates the attractor. The method maps the f(alpha) spectrum of a chaotic attractor onto that of a general two scale Cantor measure. We show that the mapping can be done for a large number of chaotic systems. In order to implement this procedure, we also propose a generalisation of the standard equations for two scale Cantor set in one dimension to that in higher dimensions. Another interesting result we have obtained both theoretically and numerically is that, the f(alpha) characterisation gives information only upto two scales, even when the underlying process generating the multifractal involves more than two scales.
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