Fu X.C., Duan Jinqiao
Infinite-Dimensional Linear Dynamical Systems with Chaoticity
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ABSTRACT. 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.