Smooth, Weakly mixing Flows on the Torus

This is joint work with Bert Hof (Caltech). Differential equations on the torus were first studied by Poincare. Later work of Denjoy, Siegel, Kolmogorov, Katok and others give today quite a good understanding of the dynamics. Recent advances in Fourier theory and spectral analysis allow us to say more on the ergodic theory of these classical flows.