科研之友
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摘要
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 W-S (x) for each X E X) is of first category and so is the 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.
- 出版日期2002-2-14
- 单位中国科学技术大学
