期刊
ERGODIC THEORY AND DYNAMICAL SYSTEMS
卷 30, 期 -, 页码 1277-1310出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0143385709000753
关键词
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资金
- ISF [1157/08]
- NNSF of China [10531010]
- 973 Project [2006CB805903]
- FANEDD [200520]
- 973 programme
Let (X, T) be a topologically transitive dynamical system. We show that if there is a subsystem (Y, T) of (X, T) such that (X x Y, T x T) is transitive, then (X, T) is strongly chaotic in the sense of Li and Yorke. We then show that many of the known sufficient conditions in the literature, as well as a few new results, are corollaries of this statement. In fact, the kind of chaotic behavior we deduce in these results is a much stronger variant of Li-Yorke chaos which we call uniform chaos. For minimal systems we show, among other results, that uniform chaos is preserved by extensions and that a minimal system which is not uniformly chaotic is PI.
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