# no closed orbits and Liapunov functions

What are some techniques to finding/picking Liapunov functions?

What does "by considering straight lines connecting fixed points show that there are no closed orbits" mean? If fixed points are saddle point, unstable node, stable node, how are there straight lines connecting the fixed points?

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For searching purposes: "Liapunov" is also spelled "Lyapunov". –  Guess who it is. Oct 16 '11 at 13:06
I presume you are looking at a specific ODE problem? The quoted text doesn't allow you to rule out periodic orbits unless you have some extra information. –  Sam Lisi Oct 17 '11 at 19:42
The word "saddle" refers to the function's behavior in the image, so there's no issue with drawing a line in the domain. –  anon Oct 17 '11 at 20:01