Logistic映射中的Pascal（Yang Hui）三角形与幂律
Pascal (Yang Hui) triangles and power laws in the logistic map
摘要：
我们指出联合发生的Pascal三角形模式和幂律标度在标准的Logistic映射，或更一般地说，在单峰映射。这些特征存在于两类分岔级联中：周期分岔和混沌带分岔。近似的帕斯卡三角形表现出的超循环直径的长度集和开放带的宽度集。此外，幂律标度沿周期性吸引子超循环位置和混沌带分裂点表现。因此，吸引子的相互积累点的加倍级联，混沌的发病，显示高斯和幂律分布。它们的组合存在意味着动力学性质的普通和特殊的物理力学描述。
英文摘要：
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic- band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.
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