  This is the first of a series of two papers. We discuss some basic problems
of the quantum kicked rotator (QKR) and review some important results in the
literature. We point out the flaws in the inverse Cayley transform method to
prove dynamic localization. When $\tau/2\pi$, where $\tau$ is the kick period,
is very close to a rational number, the localization length is larger than the
typical localization length. We analytically prove anomalous localization and
confirm it by numerical calculations. We point out open problems that need
further work.

Chaotic Dynamics