Talk:Stable manifold theorem

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Systems Mid‑importance

	Systems science portal This article is within the scope of WikiProject Systems, which collaborates on articles related to systems and systems science.SystemsWikipedia:WikiProject SystemsTemplate:WikiProject SystemsSystems articles
Mid	This article has been rated as Mid-importance on the project's importance scale.
	This article is within the field of Dynamical systems.

Daily pageviews of this article

A graph should have been displayed here but graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at pageviews.wmcloud.org

Locally?[edit]

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 article; otherwise I'll have to consult a couple of books when I get back to the office. -- Jitse Niesen (talk) 03:45, 11 March 2007 (UTC)[reply]

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 submanifolds 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. MathMartin 15:41, 11 March 2007 (UTC)[reply]