Generalized Lyapunov exponent as a unified characterization of dynamical instabilities

Takuma Akimoto, Masaki Nakagawa, Soya Shinkai, Yoji Aizawa

    研究成果: Article査読

    6 被引用数 (Scopus)


    The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent (exponential dynamical instability) is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov exponent, as a unified characterization of nonexponential and exponential dynamical instabilities in one-dimensional maps. Chaos is classified into three different types, i.e., superexponential, exponential, and subexponential chaos. Using one-dimensional maps, we demonstrate superexponential and subexponential chaos and quantify the dynamical instabilities by the Lyapunov pair. In subexponential chaos, we show superweak chaos, which means that the growth of the difference of nearby orbits is slower than a stretched exponential growth. The scaling of the growth is analytically studied by a recently developed theory of a continuous accumulation process, which is related to infinite ergodic theory.

    ジャーナルPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    出版ステータスPublished - 2015 1月 30

    ASJC Scopus subject areas

    • 凝縮系物理学
    • 統計物理学および非線形物理学
    • 統計学および確率


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