Ratner's property and mild mixing for special flows over two-dimensional rotations (Q630027)

The main result of this paper is to show that suspension flows over rotations of the torus \(\mathbb T^2\) with piecewise \(C^2\) roof functions \(f\) such that the integrals of the partial derivatives of \(f\) are non-zero are mildly mixing. The key idea is to abstract a property of Ratner's property which she used to study horocycle flows.