Second, the space of solutions to (1) is a two dimensional module over the ring of 
   functions invariant by the skew shift.
   So for  a fundamental solution to (1) (i.e. ), one has
   
   The matrix  is the monodromy matrix; it satisfies
   
   Define the shift on the cylinder  Pick 
   and fix  Setting  one checks
   
   
   The definition of the monodromy matrix immediately implies