For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent ${\lambda }_{max}>0$ holds on a shy set in the measure-theoretic sense. This exhibits that strongly monotone dynamical systems admit no observable chaos, the notion of which was formulated by L.S. Young. We further show that such phenomenon of no observable chaos is robust under the $C^1$-perturbation of the systems.

中文翻译：

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强单调动力系统中不存在可观察到的混沌及其鲁棒性

对于 Banach 空间上的强单调动力系统，我们表明最大的 Lyapunov 指数${\lambda }_{最大限度}>0$在测度论意义上保持一个害羞的集合。这表明强单调动力系统不允许任何可观察到的混沌，混沌的概念是由 LS Young 提出的。我们进一步表明，这种没有可观察到的混沌现象在$C^{\mathrm{1个}}$-系统的扰动。