Generalized shifts: unpredictability and undecidability in dynamical systems Nonlinearity 4 199-230
Generalized shifts: unpredictability and undecidability in dynamical systems Nonlinearity 4 199-230
复制标题
广义转变：动力系统中的不可预测性和不可判定性 非线性 4 199-230
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Cristopher Moore
中科院分区：
文献类型：
--
作者：
Cristopher Moore
提出了一类具有多种行为的类移位动力系统。沿着给出了三个例子，并给出了一些一般性的定义和结果.与图灵机的通信允许人们讨论可预测性和复杂性的问题。这些系统具有一种比以前在低维混沌研究中讨论的更强的不可预测性，并且许多关于其动力学的简单问题是不可判定的。作者讨论了它们产生的各种集合的复杂性，包括周期点、吸引域和时间序列。最后，他证明了它们可以嵌入R2中的光滑映射或R3中的光滑流。
A class of shift-like dynamical systems is presented that displays a wide variety of behaviours. Three examples are presented along with some general definitions and results. A correspondence with Turing machines allows one to discuss issues of predictability and complexity. These systems possess a type of unpredictability qualitatively stronger than that which has been previously discussed in the study of low-dimensional chaos, and many simple questions about their dynamics are undecidable. The author discusses the complexity of various sets they generate, including periodic points, basins of attraction, and time series. Finally, he shows that they can be embedded in smooth maps in R2, or smooth flows in R3.