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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 4, Pages 793-804
http://dx.doi.org/10.1155/S0161171288000961

Some roughness results concerning reducibility for linear difference equations

Democritus University of Thrace, School of Engineering, Xanthi 671 00, Greece

Received 20 October 1987

Copyright © 1988 Hindawi Publishing Corporation. 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

In this paper we prove first that the exponential dichotomy of linear difference equations is “rough”. Moreover we prove that if the coefficient matrix of a linear difference equation is almost periodic, then the Joint property of having an exponential dichotomy with a projection P and being reducible with P by an almost periodic kinematics similarity is “rough”.