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answered Aug 8, 2015 at 15:52

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$S^{2}$ satisfies the Poincare Bendixon theorem but this theorem is not satisfied by higher dimensional spheres.

For a related MSE post see the following.

http://math.stackexchange.com/questions/861231/extension-of-poincar%C3%A9-bendixson-theorem-to-mathbbr3

answered Aug 8, 2015 at 15:52

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