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Qmechanic ♦
Qmechanic ♦
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The Poincaré–Bendixson theoremPoincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?

The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?

The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?

Small typo.
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stafusa
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The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour ancan only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?

The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour an only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?

The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?

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fhorrobin
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Physical intuition behind Poincaré–Bendixson theorem

The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour an only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that cannot admit a strange attractor? Why does this only apply to continuous systems and not discrete ones?