Products of 2×2 matrices related to non autonomous Fibonacci difference equations

摘要

A technique to compute arbitrary products of a class of Fibonacci 2×2 square matrices is proved in this work. General explicit solutions for non autonomous Fibonacci difference equations are obtained from these products. In the periodic non autonomous Fibonacci difference equations the monodromy matrix, the Floquet multipliers and the Binet’s formulas are obtained. In the periodic case explicit solutions are obtained and the solutions are analyzed.