Title:
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Integrability and non-integrability of periodic non-autonomous Lyness recurrences
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Author:
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Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
Abstract:
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Preprint arXiv:1012.4925 |
Abstract:
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This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately. |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics -Differential equations -Differentiable dynamical systems -Periodic difference equations -Integrability -Non-integrability -Meromorphic first integrals -Chaos -Equacions diferencials -Sistemes dinàmics diferenciables -Classificació AMS::39 Difference and functional equations::39A Difference equations |
Rights:
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Document type:
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Article - Draft Other |
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