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Mathematics
Differential Equations
Dynamic Systems: Poincaré-Bendixson Theorem finite # of equilibria
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[QUOTE="Master1022, post: 6587296, member: 650268"] Thank you for responding once again. Okay - I agree. Thanks. I did make a sketch and can convince myself of the ## \alpha ## and ## \omega ## limits. I know I keep asking, but perhaps I should rephrase it to my current misunderstanding: what does the "orbits ##\gamma## with ##\alpha (\gamma) = \mathbf{x}_i ^{*} ## and ##\omega (\gamma) = \mathbf{x}_j ^{*} ##" mean in from the theorem (point 3)? Does the 'orbits ##\gamma##' mean that the positively invariant region encapsulates this heteroclitic (for example) orbit that we have sketched above? [/QUOTE]
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Dynamic Systems: Poincaré-Bendixson Theorem finite # of equilibria
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