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Damian
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« on: January 13, 2004, 04:38:26 pm »

Dear all
I would like to use the Center Manifold Theorem (CMT). Unfortunately my mathematical background is not so good and hence i have a big problem. Therefore I would like to ask you if you know any good book/website about CMT.

Thanks
Damian
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riis
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« Reply #1 on: January 13, 2004, 06:10:20 pm »

is excellent! thumb_yello It deals about a very wide range of mathematical topics, and if you're interested in other sciences, then there are several "sister" sites as well.
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jonnylane
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« Reply #2 on: January 13, 2004, 10:56:03 pm »

What is the nature of your problem you need to solve with CMT?

It's not the kind of thing you can approach with little knowledge of mathematics. I remember it being mentioned while I was studying dynamical systems, but I don't know much about it at all.

riis is right, wolfram maths is a great place to start. Any specific questions, post them here.

J.
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Damian
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« Reply #3 on: February 10, 2004, 06:53:27 pm »

My problem is that all the applcations/examples of the CMT that I found are on simple second order systems. But what about when there is a 5th order system and there is one zero eigenvalue and 4 negative?

Then the system is decomposed to Dy=g1(y,z), Dz=B*Z+g2(y,z), eig(B) <0.

Hence I have to create z1=h1(y), z2=h2(y), z3=h3(y), z4=h4(y).

Then I have to solve a complicated SYSTEM of equations to find the center manifold.  :cry:  

But then, the center manifold is found z1=0, z2=0, z3=0,z4=0  and the flow on it is Dy=0 (Dy=z3*z2-z1*z2=0).

And this is what I cannot understand!

Thanks
Damian
« Last Edit: February 11, 2004, 06:57:03 pm by Damian » Logged

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