Phase space trajectory question

[Grand]

In my lecture they give the phase space picture for a simple pendulum
http://mathematicalgarden.files.wordpress.com/2009/03/pendulum-portrait3.png?w=500&h=195

and then say that adjacent trajectories never diverge and therefore evolution is predictable. I wanted to ask, is the statement that adjacent trajectories never diverge just a consequesnce of the fact that motion of the simple pendulum is predictable, i.e. a small variation in initial conditions will not produce totally different trajectory. Or am I just being stupid and the answer is diferent?

 

[Spinnor]

Suppose two phase space paths for the pendulum crossed at a point in phase space. At that point the total energy for the two paths is the same, E = T + V. But if the paths diverge then the total energy can no longer be constant, but the total energy for an ideal pendulum is constant.

Does that fly for you?