Renormalization of matrix cocycles:
   
   Consider the matrix valued function  defined by
   
   and the skew shift on the cylinder
   
   The product we are interested in can be rewritten as
   
   We denote this cocycle by 
   Analyzing the cocycle is equivalent to analyzing the equation
   
   Therefore, we generalize the idea of a monodromy matrix introduced in previous
   works.
   First,  commutes with the translation by