Measuring the mixing efficiency in a simple model of stirring:some   analytical results and a quantitative study via Frequency Map Analysis
  We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the Numerical Analysis of the Fundamental Frequency of Laskar, we investigate numerically the break down of invariant curves as $T$ increases and we give a quantitative estimate of the efficiency of the mixing. 
Timoteo Carletti and Alessandro Margheri