科研之友
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摘要
Let (X, d) be a compact nontrivial metric space and H(X) the set of all homeomorphisms of X. A system f is an element of H(X) is said to be chaotic if some positive iteration of f is semiconjugated to the shift map s : Sigma -> Sigma. For any k not equal 0 andany f is an element of H(X), we show that f is chaotic if and only if f k is chaotic. Furthermore, we present some sufficient conditions for a system f is an element of H(X) to be chaotic. In particular, it is shown that (1) If f is an element of H(X) is chaotic in the sense of Devaney and has the shadowing property, then f is chaotic; (2) If f is an element of H(X) and g. H(X') have the shadowing property, then f xg is chaotic if and only if f or g is chaotic, where X' is a compact metric space; and (3) For a continuum X and any f is an element of H(X), if f is P-chaotic, then it is chaotic. As an application, we characterize any positive entropy system f is an element of H(T) with the shadowing property, where T is a tree.
- 出版日期2016
- 单位广东海洋大学
