The quasi-periodic kicked rotor is a one-dimensional system displaying the same metal-insulator Anderson transition than a usual 3D disordered system.  This model can be experimentally realized using a cold atomic gas, allowing for a direct measurement of the temporal dynamics.  Accurate measurements of the atomic wavefunction dynamics and the use of finite-size scaling techniques make it possible to measure with a good precision the value of the critical exponent \nu and to test its universality.  We also study the spatio-temporal evolution of the  wavefunction at the critical point, and show that it is well described at short times by self-consistent theory of localization.  At long times - probably not accessible to the present generation of experiments - large deviations are observed, related to the multifractal character of the wavefunctions.