Kolmogorov entropy, also known as metric entropy, Kolmogorov-Sinai entropy, or KS entropy, is defined as follows. Divide phase space
into 
-dimensional
hypercubes of content 
. Let 
be the probability that a trajectory is in hypercube 
at 
, 
at 
, 
at 
, etc. Then define
 |
(1)
|
where 
is the information needed to predict which hypercube
the trajectory will be in at 
given trajectories up to 
. The Kolmogorov entropy is then defined by
 |
(2)
|
The Kolmogorov entropy is related to Lyapunov characteristic exponents by
 |
(3)
|
The Kolmogorov entropy is 0 for nonchaotic motion and positive for chaotic motion.
