动力学分类法：对每个混沌吸引子进行系统分类的分类等级
Dynamical Taxonomy: some taxonomic ranks to systematically classify every chaotic attractor
摘要：
准确地描述混沌行为不是一个简单的问题，必须允许确定两个给定的混沌不变集共享或不共享的属性。根本的问题是混乱政权的分类和标签。解决这些问题对应的动态分类的发展，表现出的关键属性区分丰富的文献中讨论的各种混沌行为。从我们中的一个人最初提出的混沌层次结构开始，我们系统化了在三维和四维空间中观察到的混沌状态的描述，其中涵盖了大量已知（和不太知名）的混沌系统的例子。从李雅普诺夫指数的谱作为第一分类秩开始，我们利用从拓扑学继承的一些概念（有界环面、截面曲面、首次返回映射.）将描述扩展到更高的秩。通过对Rössler吸引子和Lorenz吸引子的广泛处理，我们将混沌吸引子分类的最高分类阶--分支流形的描述通过连接矩阵（或连接子）扩展到多分量吸引子（以亏格g <= 3的环面为界
英文摘要：
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labelling. Addressing these problems correspond to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety of chaotic behaviors discussed in the abundant literature. Starting from the hierarchy of chaos initially proposed by one of us, we systematized the description of chaotic regimes observed in three- and four-dimensional spaces, which cover a large variety of known (and less known) examples of chaotic systems. Starting with the spectrum of Lyapunov exponents as the first taxonomic ranks, we extended the description to higher ranks with some concepts inherited from topology (bounding torus, surface of section, first-return map...). By treating extensively the Rössler and the Lorenz attractors, we extended the description of branched manifold -- the highest taxonomic rank for classifying chaotic attractor -- by a linking matrix (or linker) to multi-component attractors (bounded by a torus whose genus g <= 3
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