To find global asymptotics for the coefficients of the monodromy matrix,
we recall that they are -periodic; 
so asymptotics in domains are immediately extended to strips.

One computes




where the phase and actions are




Iso-energy curve:
 
Let  be the dispersion relation i.e. inverse of the Bloch quasi-momentum.
Define


The complex curve  is the Riemann surface uniformizing