Chaos in the sense of Li-Yorke and the order of the inverse limit space  

作　　者：Jie Lü Xiangdong Ye 

机构地区：[1]Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

出　　处：《Chinese Science Bulletin》1999年第11期988-992,共5页

摘　　要：Let l=[0,1] and ω₀ be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2ⁱ: i∈{0}∪N}. It is known that the order of （l, f） is ω₀ or ω₀ + 1. It is shown that the order of the inverse limit space （l, f） is ω₀ （resp. ω₀ + 1） if and only if f is not （resp. is） chaotic in the sense of Li-Yorke.LetI= [0, 1] and ω0 be the first limit ordinal number. Assume thatf: 1→- 1 is continuous, piece-wise monotone and the set of periods off is |2′: iε |0|U|. It is known that the order of (1, 1) is ω0 or w0 + 1. It is shown that the order of the inverse limit space (1, f) is ω0 (resp. ω0 + 1) if and only iff is not (resp. is) chaotic in the sense of Li-Yorke.

关 键 词：inverse limit space order of hereditarily decomposable chainable CONTINUA CHAOS in the SENSE of LI-YORKE REGULAR RECURRENT point. 

分 类 号：O415.5[理学—理论物理]