1998/05/25 by Xinchu Fu, Xin-Chu Fu, Fu, Xin-Chu +2
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9805022
LaTeX file. Journal of Nonlinear Science, to appear
arxiv created 1998/05/25 · arxiv updated 2009/11/30
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.