Infinite-Dimensional Linear Dynamical Systems with Chaoticity
- First Online:
- Cite this article as:
- -C. Fu, X. & Duan, J. J. Nonlinear Sci. (1999) 9: 197. doi:10.1007/s003329900069
- 66 Downloads
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.