On periodic solutions of 2-periodic Lyness difference equations
| Contribuinte(s) |
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya. CODALAB - Control, Dinàmica i Aplicacions |
|---|---|
| Data(s) |
10/05/2012
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| Resumo |
We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_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) different from (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 is not equal to b, then any odd period, except 1, appears. Preprint Preprint |
| Identificador | |
| Idioma(s) |
eng |
| Direitos |
Open Access |
| Palavras-Chave | #Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències #Difference equations #Difference equations with periodic coefficients #Elliptic curves #Lyness' type equations #QRT maps #Rotation number #Periodic orbits #Equacions en diferències #Classificació AMS::39 Difference and functional equations::39A Difference equations |
| Tipo |
info:eu-repo/semantics/other |
