Mixing for some classes of special flows over rotations of the circle (Q1324668)

In Arnol'd's paper [\textit{V. I. Arnol'd}, Funct. Anal. Appl. 25, No. 2, 81--90 (1991); translation from Funkts. Anal. Prilozh. 25, No. 2, 1--12 (1991; Zbl 0732.58001)] it was shown that in general position the phase space of a Hamiltonian system with a multiple-valued Hamiltonian function on the two-dimensional torus can be decomposed into a finite number of cells filled by periodic trajectories and one ergodic component; over this component the phase flow is isomorphic to a special flow over rotation of the circle defined by a function with a finite number of asymmetrical logarithmic singularities. In this connection, the question of mixing for such flows arises. Our purpose is to give a positive answer to this question.