Looking at this fraction is a little bit different than looking at the other complex fractions that we've dealt with. However, we can make it look like the other complex fractions. But first of all, ...

We consider the irrational Aubry-Mather scts of an exact sympleetic monotone C¹ twist map of the two-dimensional annulus, introduce for them a notion of "C¹-regularity" (related to the notion of ...