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I'm working from memory here, but I thought that W_u and W_s are only a manifold locally around the fixed point? Can't W_u be with the shape of the figure 8, in the presence of homoclinic connections? I'm hoping that somebody knows immediately what I mean and is able to either shut me up or amend the
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of the original manifold. One can also define global stable/unstable manifolds and equip them with a differentiable structure but in general not as submanifolds of the original manifold.
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I am not an expert on this topic so any help is appreciated :). As far as I know the theorem provides you with local, differentiable
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article; otherwise I'll have to consult a couple of books when I get back to the office. --
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