Fu X.C., Duan Jinqiao
Infinite-Dimensional Linear Dynamical Systems with Chaoticity
(41K, LaTeX)

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.