科研之友
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摘要
This paper introduces the concept of Kato chaos to linear dynamics and its induced dynamics. This paper investigates some properties of Kato chaos for a continuous linear operator T and its induced operators T over bar . The main conclusions are as follows: (1) If a linear operator is accessible, then the collection of vectors whose orbit has a subsequence converging to zero is a residual set. (2) For a continuous linear operator defined on Frechet space, Kato chaos is equivalent to dense Li-Yorke chaos. (3) Kato chaos is preserved under the iteration of linear operators. (4) A sufficient condition is obtained under which the Kato chaos for linear operator T and its induced operators T over bar are equivalent. (5) A continuous linear operator is sensitive if and only if its inducing operator T over bar is sensitive. It should be noted that this equivalence does not hold for nonlinear dynamics.
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单位吉林大学
