Smooth singular flows in dimension 2 with the minimal self-joining property (Q1006433)

This paper extends our understanding of the existence of smooth models for subtle abstract measure-theoretic ergodic phenomena. The main result is that if \(\alpha_1/\alpha_2\) is an irrational with bounded partial quotients, then the flow on the \(2\)-torus defined by the quasi-periodic Hamiltonian satisfying \(H(x+m,y+n)=H(x,y)+m\alpha_1+n\alpha_2\) has velocity changes that are singular flows with an ergodic component which has minimal self-joinings. The proof involves a careful analysis of joinings between certain flows built under functions.