Semicontinuity of the derivative of the rotation number

with Rafael Obaya,

C. R. Math. Acad. Sci. Paris, Serie I

This note is concerned with the study of the one-dimensional Schrödinger

equation. Let A

admits an invariant measure with square integrable density function. We

prove the continuous variation of an adequate family of linear measures

and deduce that the derivative of the rotation number is lower

semicontinuous on A