This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical finding has implications for many applications in which chaotic dynamics plays an important role. It suggests, for example, that we can control the climate through subtle perturbations. It also suggests that numerical simulations of chaotic dynamics, such as turbulent flows and global atmosphere and ocean circulation, may fail to predict the true long-term or statistical behavior.

中文翻译：

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关于通过阴影找到非物理解的可能性

本文证明了阴影解决方案几乎可以肯定是非物理的。这一发现使关于混沌系统中的微扰只能对其统计行为产生很小影响的论点无效。这一理论发现对混沌动力学起重要作用的许多应用具有重要意义。例如，这表明我们可以通过微妙的干扰来控制气候。这也表明，混沌动力学的数值模拟（例如湍流，全球大气和海洋环流）可能无法预测真正的长期或统计行为。