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[讨论] Any difference between Smooth and nonsmooth chaos?
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本人从事一些混沌学方面的研究，感觉混沌学可以归为“理工版”。 所以想把我的一些对于smooth chaos 和 nonsmooth chaos 的一些看法整理如下。由于原来使用的是英文，就不翻译从中文了（有些术语翻译起来比较麻烦）。 如果有哪位感兴趣，我们可以讨论一下。在此先谢了。 Given a smooth dynamical system, two initially-nearby orbits remain close as least in a short time interval. However, a chaotic attractor is an asymptotic product of the system. So it is very doubtful that smoothness plays a vital role in the occurrence of a chaotic attractor. It appears more natural that smoothness plays no role in this phenomenon. If this is true, rigorous proof regarding to chaos based on smoothness (or more weakly, continuity) is merely a tool to show the existence of chaos, in another word, they are merely sufficient, but not necessary. If we deem this is correct, then we may believe that there must be some deeper roles underlying the existence of chaos, and hopefully these roles are also applicable to non-smooth chaos. This seems quite natural and appealing to me. |
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