Abstract
An exact map of the probability distribution function for the kicked rotor is generated by solving Liouville's equation for any arbitrary initial condition and kicking strength. This solution is compared to the analogous quantum map. In this manner we compare two linear partial differential equations describing the evolution of wave functions in Hilbert space. This exact map is also compared to Chirikov's standard map generated from the canonical equations of motion. As expected, the classical map for the probability distribution function is chaotic for large kicking potentials. The practical reversibility of Liouville's equation is compared to Schr\"odinger's equation and the standard map.
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