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

Luís, Rafael; Oliveira, Henrique M.

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http://hdl.handle.net/10400.13/3768

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Authors

Luís, Rafael

Oliveira, Henrique M.

Abstract(s)

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 dif ference 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.

Keywords

Matrix products Fibonacci sequences Non-autonomous difference equation Linear recurrences Monodromy matrix Floquet multipliers . Faculdade de Ciências Exatas e da Engenharia

URI

http://hdl.handle.net/10400.13/3768

Citation

Luís, R., & Oliveira, H. M. (2014). Products of 2× 2 matrices related to non autonomous Fibonacci difference equations. Applied Mathematics and Computation, 226, 101-116. 10.1016/j.amc.2013.09.075