  We show that the typical dynamical system sometimes begins to behave like a
non-deterministic system with a small classical entropy, and this behavior
lasts an extremely long time, until the system starts decreasing entropy. Then
again it will become almost non-deterministic for a very very long time, but
with more smaller classical entropy. Playing on this fact and considering
sigma-compact families of measure-preserving zero-entropy transformations, for
example, the rectangle exchange transformations, we choose the Kushnirenko
entropy so that it is equal to zero for the transformations under
consideration, but is infinite for the generic transformation.
