vault backup: 2024-11-18 13:30:02

2024-11-18 13:30:02 -05:00 · 2024-11-18 13:30:02 -05:00 · faebd5d307
commit faebd5d307
parent 177a43a140
1 changed files with 2 additions and 2 deletions
--- a/Contraction.md
+++ b/Contraction.md
@ -1,7 +1,7 @@
 Lorenz system is dissapative. This means:
 - Volume in phase space contracts with flow?
 This introduces some questions... How do volumes evolve?
-
+n
 Suppose a surface $S(t)$ encloses volume $V(t)$, with normal vectors pointing away from the surface ($\vec{n}$). 

 A trajectory starts on S. let them evolve for $dt$. With a flux vector $\vec{f}$, we have 
@ -18,4 +18,4 @@ Limiting set will consist of
 - fixed points
 - limit cycles
 - strong attractors
-Proving which type something will end up on 
+Proving which type something will end up on is much harder. But, repellers will always result in a positive $\dot V$.