Talk:Hartman–Grobman theorem

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Systems Mid‑importance

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Discussion

"hyperbolic equilibrium point is qualitatively the same as the behaviour of its linearization near this equilibrium point provided that no eigenvalue of the linearization has its real part equal to 0" Isn't hyperbolic equilibrium defined by the fact that the linearisation doesn't have any eigenvalues on the imaginary axis? Really random name (talk) —Preceding undated comment added 23:51, 1 November 2013 (UTC)[reply]

Yes. I think that given that it defines a fixed point as where f(u)=0, this means that it's using the f=F-id(x) definition for the function. This should be made clear in the article. Fephisto (talk) 09:48, 7 October 2014 (UTC)[reply]

1. In the first paragraph: "is unreasonably effective in predicting qualitative patterns"

Shouldn't this read "reasonably" instead of "unreasonably"?

2. In the "Main Theorem" section: "conjugate by the smooth map U=h(u) to the flow"

Shouldn't "U=h(u)" read simply "h"?

3. In the example: "This system has an equilibrium at the origin, that is u^*=0, among others not analysed here."

The origin is the only real equilibrium point, so the phrase "among others not analysed here" is inappropriate. — Preceding unsigned comment added by Louis1952 (talk • contribs) 07:01, 2 September 2015 (UTC)[reply]