Estimating the spectral measures of
smooth flows on the torus
Introduction and the result.
 Title of the talk
 ODE's on the torus
 History of the problem
 The main result
Three pillars: ergodic theory, Fourier theory, measure theory
 Periodic Approximations
 Strichartz theorem
 Decomposition of measures
A general result and the idea of the proof
 A result on the dimension
 The core of the proof
 Generic continuity
 A generalistion of a thm of Katok
An application for Hamiltonian systems and open questions
 Weakly mixing tori of Hamilt.
 Open questions
