Floquet theory for second order linear homogeneous difference equations
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In this paper we provide a version of the Floquet’s theorem to be applied to any second order difference equations with quasi-periodic coefficients. To do this we extend to second order linear difference equations with quasi-periodic coefficients, the known equivalence between the Chebyshev equations and the second order linear difference equations with constant coefficients. So, any second order linear difference equations with quasi-periodic coefficients is essentially equivalent to a Chebyshev equation, whose parameter only depends on the values of the quasi-periodic coefficients and can be determined by a non-linear recurrence. Moreover, we solve this recurrence and obtaining a closed expression for this parameter. As a by-product we also obtain a Floquet’s type result; that is, the necessary and sufficient condition for the equation has quasi-periodic solutions.
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Difference Equations and Applications on 05/11/2015, available online: http://www.tandfonline.com/10.1080/10236198.2015.1100609
CitationEncinas, A., Jiménez, M.J. Floquet theory for second order linear homogeneous difference equations. "Journal of difference equations and applications", 2016, v. 22, n. 3, p. 353-375