Advances in Difference Equations
Volume 2011 (2011), Article ID 571935, 23 pages
doi:10.1155/2011/571935
Research Article

Generalized Zeros of 2 × 2 Symplectic Difference System and of Its Reciprocal System

Ondřej Došlý1 and Šárka Pechancová2

1Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Žižkova 17, 602 00 Brno, Czech Republic

Received 1 November 2010; Accepted 3 January 2011

Academic Editor: R. L. Pouso

Copyright © 2011 Ondřej Došlý and Šárka Pechancová. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish a conjugacy criterion for a 2 × 2 symplectic difference system by means of the concept of a phase of any basis of this symplectic system. We also describe a construction of a 2 × 2 symplectic difference system whose recessive solution has the prescribed number of generalized zeros in ℤ .