Abstract
This paper mainly discusses how Devaney chaos and Li-Yorke sensitivity carry over to product systems. First, two results on the periodic points of product systems are obtained. By using them, the following two results are Proved: (1) A finite product system is mixing and Devaney chaotic if and only if each factor system is mixing and Devaney chaotic. (2) An infinite product map Î i=1âfi is mixing and Devaney chaotic if and only if each factor map fi is mixing and Devaney chaotic and sup {min P(fi): i â â} < + â, where P(fi) is the set of all periods of fi. Besides, we obtain that the product system is Li-Yorke sensitive (sensitive) if and only if there exists a factor system that is Li-Yorke sensitive (sensitive).
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