, Volume 9, Issue 2, pp 197-211
Date: 01 Jan 1999

Infinite-Dimensional Linear Dynamical Systems with Chaoticity

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The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fr├ęchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.

Received January 27, 1997; second revision received August 8, 1997; final revision received January 12, 1998