Let l=[0,1] and ω<sub>0</sub> be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2<sup>i</sup>: i∈{0}∪N}. It is known th...Let l=[0,1] and ω<sub>0</sub> be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2<sup>i</sup>: i∈{0}∪N}. It is known that the order of （l, f） is ω<sub>0</sub> or ω<sub>0</sub> + 1. It is shown that the order of the inverse limit space （l, f） is ω<sub>0</sub> （resp. ω<sub>0</sub> + 1） if and only if f is not （resp. is） chaotic in the sense of Li-Yorke.展开更多
文摘Let l=[0,1] and ω<sub>0</sub> be the first limit ordinal number. Assume that f:l→l is continuous, piece-wise monotone and the set of periods of f is {2<sup>i</sup>: i∈{0}∪N}. It is known that the order of （l, f） is ω<sub>0</sub> or ω<sub>0</sub> + 1. It is shown that the order of the inverse limit space （l, f） is ω<sub>0</sub> （resp. ω<sub>0</sub> + 1） if and only if f is not （resp. is） chaotic in the sense of Li-Yorke.
