A transformation for symplectic systems and the definition of a focal point

We examine transformations for symplectic difference systems and Riccati difference operators connected with permutations of rows of a conjoined basis. The concept of an integration path for a conjoined basis is introduced to formulate the definition of a focal point and the disconjugacy criteria and state Sturmʹs separation theorems in terms of solutions of the transformed Riccati equation.