Physical pendulum in phase space

Hi,
I found out this paper
http://www.pha.jhu.edu/~javalab/pend...t/pendulum.pdf
with this animation
http://www.pha.jhu.edu/~javalab/pend...t/pendula.html

At first there is written there, that the area of possible states in some range of energies
of pendulum in phase space is conserved due to Liouville's theorem. But at the end there
is all new bigger area uniformly filled up.
So both can't be right, and I thing that the area in the phase should be conserved. But don't
know hot to solve the argument with uniformly filled up the new bigger area which is in agreement
with equillibrium statistical physics of microcanonical ensembles . .
Thanks a lot for any response!