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...m of infinite ordinary differential equations. Here Hsloc(R n) does not have a countable base. In fact, often the unstable, center and stable subspaces in Hsloc(R n) are not separated from each other =-=[8]-=-. Even though it is challenging to study, Hsloc(R n) is often the natural phase space in applications, for example, in fluid dynamics. Take the plane Couette flow as the specific example. The plane Co...