Rotation number of the linear Schrödinger equation with discontinuous almost periodic potentials

In this talk, based on the celebrated paper [R. Johnson and J. Moser, Comm. Math. Phys., 1982], we will recover the rotation numbers of the Schrödinger equation. The essential elements in the proof are positive homogeneity and almost periodicity. From this point of view, the concept of rotation numbers may be introduced in the case of discontinuous potentials. Moreover, we will show the optimal estimate of rotation numbers in such case.