how would i start going about proving that if p belongs to the global manifold then the flow of p tends to the hyperbolic saddle point as t (time) tends to infinity?
intuitively the problem makes sense as p would also belong to the flow of the local stable manifold which goes towards the hyperbolic saddle point as t increases. Not sure how to prove that mathematically or is it acceptable to explain it like this.
got another one asking if the unstable and stable manifolds for a hyperbolic point can intersect at a point which is not a fixed point. Again intuitively im thinking no because it would mean there would be an intersection between the flow of local stable/unstable manifolds which I don't think is possible?
Thanks in advance
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Kim-Jong-Illest
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- 07-11-2015 13:08
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ghostwalker
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- 07-11-2015 13:48
(Original post by Kim-Jong-Illest)
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This isn't the best forum to post on. I suggest reposting on the maths forum - a subforum of this one. Mods can move threads, but it usually takes a few hours. May still take a while to get a useful response, even there. -
ghostwalker
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- 08-11-2015 09:35
BUMP - as this thread's now been moved, and is worthy of some knowledgeably person's attention.
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Gregorius
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- 09-11-2015 08:45
(Original post by Kim-Jong-Illest)
how would i start going about proving that if p belongs to the global manifold then the flow of p tends to the hyperbolic saddle point as t (time) tends to infinity?
intuitively the problem makes sense as p would also belong to the flow of the local stable manifold which goes towards the hyperbolic saddle point as t increases. Not sure how to prove that mathematically or is it acceptable to explain it like this.
got another one asking if the unstable and stable manifolds for a hyperbolic point can intersect at a point which is not a fixed point. Again intuitively im thinking no because it would mean there would be an intersection between the flow of local stable/unstable manifolds which I don't think is possible?
Thanks in advance
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