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Título:	Floquet theory for second order linear homogeneous difference equations
Autor/a:	Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José
Otros autores:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes
Abstract:	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
Abstract:	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.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències -Floquet theory -Difference equations -Difference equations -Floquet theory -Periodic sequences -Chebyshev polynomials -Equacions en diferències -Classificació AMS::39 Difference and functional equations::39A Difference equations -Classificació AMS::11 Number theory::11B Sequences and sets -Classificació AMS::33 Special functions::33C Hypergeometric functions
Derechos:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión presentada Artículo
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