Singular comparison theorems for discrete symplectic systems

We present new relations connecting the number of focal points of conjoined bases of eventually disconjugate symplectic difference systems with different coefficient matrices which obey the so-called majorant condition at infinity. For the case of controllable (near infinity) symplectic systems we investigate connections between the number of focal points of their recessive solutions. The results of the paper are based on the concept of minimal and maximal solutions of the associated Riccati matrix difference equations and the comparative index theory for discrete symplectic systems.