A Sturmian separation theorem for symplectic difference systems

We establish a Sturmian separation theorem for conjoined bases of 2n-dimensional symplectic difference systems. In particular, we show that the existence of a conjoined basis without focal points in a discrete interval (0,N +1] implies that any other conjoined basis has at most n focal points (counting multiplicities) in this interval. © 2006 Published by Elsevier Inc