Infinite-Dimensional Linear Dynamical Systems with Chaoticity
chao-dyn
2007-05-23 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.chao-dyn/9805022,
title = {Infinite-Dimensional Linear Dynamical Systems with Chaoticity},
author = {Xin-Chu Fu and Jinqiao Duan},
journal= {arXiv preprint arXiv:chao-dyn/9805022},
year = {2007}
}
Comments
LaTeX file. Journal of Nonlinear Science, to appear