SINGULARITY CONFINEMENT AND CHAOS IN DISCRETE SYSTEMS
SINGULARITY CONFINEMENT AND CHAOS IN DISCRETE SYSTEMS
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DOI：
10.1103/physrevlett.81.325
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发表时间：
1997-11
影响因子：
8.6
通讯作者：
J. Hietarinta;C. Viallet
中科院分区：
文献类型：
--
作者：
J. Hietarinta;C. Viallet
我们给出了一些二阶映射，它们通过了通常用于识别可积离散系统的奇点限制检验，但它们仍然是不可积的。作为一种更灵敏的可积性检验，我们提出了利用迭代次数的增长来分析映射的复杂性(“代数熵”)：可积性与多项式增长有关，而对于混沌系统，一般增长是指数增长的。
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the analysis of the complexity (``algebraic entropy'') of the map using the growth of the degree of its iterates: integrability is associated with polynomial growth while the generic growth is exponential for chaotic systems.