Abstract
For a large class of discrete matrix difference equations many qualitative problems remain unsolved. The companion matrix factorization is applied here to the shift matrices associated to linear non-autonomous area-preserving maps. It permits us to introduce second order linear difference equations, which provide a faster computation of the transition matrices with respect to numerical algorithms based on the standard product of matrices. In addition, compact representations for the main elements of these discrete planar systems can be provided when using the well-known solutions of linear difference equations. Some properties and applications of current interest are presented.
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