Arnold's cat,
invented by
Vladimir Arnold,
shows the time evolution of an image in the
phase space
of a
dynamical system.
The
discrete map
corresponds to fixed time intervals after which the image is observed.
(The basic geometry being that of a
torus, the matrix has to satisfy
the condition of volume preservation: det(A)=1)
Since the points of the image are finite and the map is discrete, the
image will eventually return to its original form. This illustrates the
recurrence theorem
of
Henri Poincaré,
which states that any dynamical system will return arbitrary close to its
initial state after a certain time, thus apparently contradicting laws involving
entropy
and even more contradicting our everyday experience that any
moment, once passed, is irretrievable.