  We use spin coherent states to compare classical and quantum evolution of a
simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic
behavior in the classical limit. The spin coherent states are employed to
define a phase-space quasidistribution for quantum states (P-representation).
It can be, in principle, used for a direct comparison of the quantum and
classical dynamics, where on the classical level one deals with the classical
distribution function on the classical phase space. In the paper, we presented
a different way by comparing evolution of appropriately defined moments of
classical and quantum distributions, in particular the one-step propagators of
the moments.
