Infinite-Dimensional Linear Dynamical Systems with Chaoticity |
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| Authors: | X -C Fu J Duan |
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| Institution: | (1) Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK, and Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, People's Republic of China, GB;(2) Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA, US |
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| Abstract: | Summary. 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 Fréchet 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 |
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| Keywords: | , infinite-dimension, linearity, chaoticity |
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