Journal of Nonlinear Science

, Volume 9, Issue 2, pp 197–211

Infinite-Dimensional Linear Dynamical Systems with Chaoticity

  • X. -C. Fu
  • J. Duan

DOI: 10.1007/s003329900069

Cite this article as:
-C. Fu, X. & Duan, J. J. Nonlinear Sci. (1999) 9: 197. doi:10.1007/s003329900069


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.

Key words. infinite-dimension, linearity, chaoticity 

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • X. -C. Fu
    • 1
  • J. Duan
    • 2
  1. 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 ChinaGB
  2. 2.Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USAUS

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