We analyze the behavior of two quantum dynamical entropies in
connection with the classical limit. Using strongly chaotic
classical dynamical systems as models (Arnold Cat Maps and Sawtooth
Maps), we also propose a discretization procedure that resembles
quantization; even in this case, studies of quantum dynamical entropy
production are carried out and the connection with the continuous
limit is explored. In both case (quantization and discretization) the
entropy production converge to the Kolmogorov-Sinai invariant on
time-scales that are logarithmic in the quantization (discretization)
parameter.
