It is a short but rich article that covers many subjects beginning with the derivation and ending by a remark about a quantum version of the Zaslavsky map. The map generates a family of dynamical systems with a wide spectrum of dynamics. In particular it contains systems with strange chaotic attractors, undergoes many bifurcations etc. The article is written well, and it can be published without changing.
Nevertheless, I believe that it would be worth to add the following sentence, for example at the end of the section Chaotic Attractors: "One of the reason of the popularity and importance of the Zaslavsky map is that it appears as a basic model in many problems of non-linear dissipative dynamics; for instance, in dynamical systems undergoing the saddle-node bifurcation while subjected to small periodic perturbations (Arnold, Afraimovich, Il'yashenko, Shilnikov, Dynamical Systems V), in sytems with torus break-down, etc."