On periodic solutions of 2-periodic Lyness difference equations
We study the existence of periodic solutions of the non-autonomous periodic Lyness'recurrence un+2 = (an + un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150643 |
| Acceso en línea: | https://ddd.uab.cat/record/150643 https://dx.doi.org/urn:doi:10.1142/S0218127413500715 |
| Access Level: | acceso abierto |
| Palabra clave: | Difference equations with periodic coefficients Elliptic curves Lyness' type equations QRT maps Rotation number Periodic orbits |
| Sumario: | We study the existence of periodic solutions of the non-autonomous periodic Lyness'recurrence un+2 = (an + un+1)/un, where {an}n is a cycle with positive values a,b and with positive initial conditions. It is known that for a = b = 1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a, b) 6= (1, 1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a 6= b, then any odd period, except 1, appears. |
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