Infinite-Dimensional Linear Dynamical Systems with Chaoticity

Details Infinite-Dimensional Linear Dynamical Systems with Chaoticity Infinite-Dimensional Linear Dynamical Systems with Chaoticity

1998-05-25

arxiv.org/abs/chao-dyn/9805022v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX file. Journal of Nonlinear Science, to appear

Scientific paper

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\'{e}chet 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.

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