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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Generalized Zeros of 2 × 2 Symplectic Difference System and of Its Reciprocal System | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 571935 23 pages doi 10.1155 2011 571935 Research Article Generalized Zeros of 2 X 2 Symplectic Difference System and of Its Reciprocal system Ondrej Dosly1 and Sarka Pechancova2 1 Department of Mathematics and Statistics Masaryk University Kotlarska 2 611 37 Brno Czech Republic 2 Department of Mathematics and Descriptive Geometry Faculty of Civil Engineering Brno University of Technology Zizkova 17 602 00 Brno Czech Republic Correspondence should be addressed to Ondrej Dosly dosly@math.muni.cz Received 1 November 2010 Accepted 3 January 2011 Academic Editor R. L. Pouso Copyright 2011 O. Dosly and S. Pechancova. 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. We establish a conjugacy criterion for a 2 X 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 X 2 symplectic difference system whose recessive solution has the prescribed number of generalized zeros in z. 1. Introduction The main aim of this paper is to establish a conjugacy criterion for the 2 X 2 symplectic difference system xk 1 xk I 1 Sk I z k c zz Uk 1 Uk S where Sk k dC with real-valued sequences a b c and d is such that detSk akdk -bkck 1 for every k cTZ. Recall that under this condition the matrix S is symplectic. Generally a 2n X 2n matrix S is symplectic if STJS Jz J 0 f z V 0 1.1 2 Advances in Difference Equations 1 being the n X n identity matrix and this conditions reduces just to the condition det S 1 for 2 X 2 matrices. We introduce concepts of the first and second phase of any basis of system S and we study some of their properties. We generalize results introduced in 1-4 for a Sturm-Liouville difference equation and we describe how to construct a 2 X 2 .
