GENERALIZED SHIFTS - UNPREDICTABILITY AND UNDECIDABILITY IN DYNAMIC-SYSTEMS

被引：114

作者：

MOORE, C

机构：

[1] Dept. of Phys., Cornell Univ., Ithaca, NY

来源：

NONLINEARITY | 1991年 / 4卷 / 02期

关键词：

D O I：

10.1088/0951-7715/4/2/002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 us 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. We discuss the complexity of various sets they generate, including periodic points, basins of attraction, and time series. Finally, we show that they can be embedded in smooth maps in R2, or smooth flows in R3.

引用

页码：199 / 230

页数：32

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