Shadowability of statistical averages in chaotic systems

Y C Lai, Z H Liu, G W Wei, C H Lai, Ying-Cheng Lai

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Abstract

We ask whether statistical averages in chaotic systems can be computed or measured reliably under the influence of noise. Situations are identified where the invariance of such averages breaks down as the noise amplitude increases through a critical level. An algebraic scaling law is obtained which relates the change of the averages to the noise variation. This breakdown of shadowability of statistical averages, as characterized by the algebraic scaling law, can be expected in both low- and high-dimensional chaotic systems.

Original languageEnglish
Article number184101
Pages (from-to)-
Number of pages4
JournalPhysical Review Letters
Volume89
Issue number18
DOIs
Publication statusPublished - 28 Oct 2002

Keywords

  • UNSTABLE DIMENSION VARIABILITY
  • ON-OFF INTERMITTENCY
  • TRAJECTORIES
  • OSCILLATORS
  • SADDLES
  • SETS

Cite this

Lai, Y. C., Liu, Z. H., Wei, G. W., Lai, C. H., & Lai, Y-C. (2002). Shadowability of statistical averages in chaotic systems. Physical Review Letters, 89(18), -. [184101]. https://doi.org/10.1103/PhysRevLett.89.184101