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/sci/ - Science & Math

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11769220 No.11769220 [Reply] [Original]

So my professor has taught us that if the Jacobian of the function f of an ODE (t,x)'=f(t,x) evaluated at an stationary point has zero as one of its eigenvalues, then we cannot use the linear approximation to determine its stability.

However, if there are some non-zero eigenvalues (e.g. it's got 3 eigenvalues and only one of them is 0), can I say anything about the stability of the system around such stationary point?

>> No.11769286
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11769286

new kurisu thread?

>> No.11769311

>>11769220
I don't know how to answer your question, but is the answer drawing an apostrophe?

20 > 30'
20 > d/dx 30
20 > 0

>> No.11769315
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11769315

>>11769220
Checkmate, atheists

>> No.11769503

>>11769311
Just draw a point. 20 > 3.0

>> No.11769793
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11769793

>>11769286
Yes. For science.

>> No.11770079
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11770079

>>11769793
Damn that's a cute scientist.

>> No.11770121

check Hartman–Grobman theorem,

>> No.11770126

oh and why on earth are you all weebs?!

>> No.11770141

Where IS the bitch of my intellect and intensity anyway? You'd think she'd be able to be more available or on-demand.

>*screams into every meditating person's silence for... I dunno, let's just say it is eternity and go from there*

>> No.11770150

>>11770126
You have to go back.

>> No.11770382

>>11770150
go back where?

>> No.11770392

>>11770079
why are her tits blushing

>> No.11770407 [DELETED] 
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11770407

For me, it's the icosahedron.

>> No.11770470
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11770470

>>11769220
Finally solved on of these stupid things, yesh

>> No.11770528

>>11770126
Anime website.

>> No.11770688

>>11769286
Hahahahaha didnt expect that.

>> No.11770938

>>11769220
20 > 8.0

>> No.11771700
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11771700

>> No.11771810

you can calculate the center manifold as the next best thing to a linear approximation, but once you have at least 1 zero eigenvalues you can have all sorts of cases where the linear approximation is anywhere between accurate or completely unhelpful