Comments on the non-stationary chaos

Y. Aizawa

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Non-stationary chaos is a universal phenomenon in non-hyperbolic dynamical systems. Basic problems regarding the non-stationarity are discussed from ergodic-theoretical viewpoints. By use of a simple system, it is shown that `the law of large number' as well as `the law of small number' break down in the non-stationary regime. The non-stationarity in dynamical systems proposes a crucial problem underlying in the transitional region between chance and necessity, where non-observable processes behind reality interplay with observable ones. The incompleteness of statistical ensembles is discussed from the Karamata's theory. Finally, the significance of the stationary/non-stationary interface is emphasized in relation to the universality of 1/f fluctuations.

Original languageEnglish
Pages (from-to)263-268
Number of pages6
JournalChaos, Solitons and Fractals
Volume11
Issue number1
DOIs
Publication statusPublished - 2000 Jan

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics

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