摘要
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.
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.
