Talk:Poincaré–Bendixson theorem

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[edit] Assumption

Doesn't this make the assumption that the 2 dimensional space involved has a nice clean topology and geometry? I ask this because it intuitively appears that if you have a closed 2 dimensional hyperbolic space, two close rays would be sensitive to their initial differences and separate sharply. This would show up as the rays producing different homotopies as they traversed the space. (Of course, this could be represented as a discrete system equivalent to the continuous one, but the continuous one is still available.)

Good point about the topology, I edited the article to reflect this.--Experiment123 03:25, 3 March 2006 (UTC)