Comments on the non-stationary chaos

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 Karamataʹs theory. Finally, the significance of the stationary/non-stationary interface is emphasized in relation to the universality of 1/f fluctuations.