Talk:Lyapunov function: Difference between revisions

Revision as of 20:05, 6 June 2007

Revision as of 16:40, 4 July 2007

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Definitions such as these may be appropriate for Mathworld, but they don't belong in an open, global community such as Wikipedia. Is anyone aware that persons other than graduate students and elitist Mathematicians reference these articles? Most of the mathematical definitions I've read on here are written in the most advanced, arcane way possible... heaven forbid we ever write something accessible to the "laymen" out there who seek useful descriptions for the mathematical entities they encounter.

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For me it is important, that an article is ''mathematically clear''. <br>I don't see the point of having easy to read articles which do not take into consideration some details which may become important and are of course not that easy to understand. <br>

I changed the following:<br>

- "Lypaunov functions can be used to prove the stability or instability of fixed points in dynamical systems and autonomous differential equations." <br>This is wrong, a Lyapunov function by definition proves the stability of a certain equilibrium. Otherwise it is a Lyapunov candidate funciton. And there is no way to prove instability with a Lyapunov function.

Further on, I introduced a definition of the Lyapunov-candidate-function and a (as i hope) clear version of the "Basic Lyapunov theorems for autonomous systems", which can be used to prove stability of an equilibrium point of such a system.

<br>([[User:FredTschanz|FredTschanz]] 16:40, 4 July 2007 (UTC))