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期刊论文
Devaney's chaos or 2-scattering implies Li-Yorke's chaos
Topology and its Applications 117(2002)259-272,-0001,():
Let X be a compact metric space, and let f: X→X be transitive with X infinite. We show that each asymptotic class (or the stable set Ws (x) for each x ∈ X) is of first category and so is th asymptotic relation. Moreover, we prove that if the proximal relation is dense in a neighbourhood of some point in the diagonal then f is chaotic in the sense of Li-Yorke. As applications we obtain that if f contains a periodic point, or f is 2-scattering, then f is chaotic in the sense of Li-Yorke. Thus, chaos in the sense of Devaney is stronger than that of Li-Yorke. Elsevier Science B.V. All rights reserved.
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