Self-similarity of the quadratic exponential matrix cocycle:
   
   As the matrix defining the cocycle is unimodular, one has 
   Without loss of generality, we assume that  so that 
   With this in mind, we denote the matrix by 
   Our main technical result is 
   
   
   
   
   
   The proof of Theorem 2 is not elementary. The construction is closely related to
   the theory of minimal entire solutions of difference equations in the complex.