Now showing items 1-6 of 6

  • On 2- and 3-periodic Lyness difference equations 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2011-06-09)
    Article
    Open Access
    We describe the sequences {xn}n given by the non-autonomous second-order Lyness difference equations xnþ2 ¼ ðan þ xnþ1Þ=xn, where {an}n is either a 2-periodic or a 3- periodic sequence of positive values and the initial ...
  • On periodic solutions of 2-periodic Lyness difference equations 

    Bastien, Guy; Mañosa Fernández, Víctor; Rogalski, Marc (2012-01-04)
    Other
    Open Access
    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 ...
  • On Poncelet's maps 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2010-08-08)
    Article
    Open Access
    Given two ellipses, one surrounding the other one, Poncelet introduced a map P from the exterior one to itself by using the tangent lines to the interior ellipse. This procedure can be extended to any two smooth, nested ...
  • On two and three periodic Lyness difference equations 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2009-12-26)
    External research report
    Open Access
    We describe the sequences {x_n}_n given by the non-autonomous second order Lyness difference equations x_{n+2}=(a_n+x_{n+1})/x_n, where {a_n}_n is either a 2-periodic or a 3-periodic sequence of positive values and the ...
  • Resonance tongues and spectral gaps in quasi-periodic schrödinger operators with one or more frequencies. A numerical exploration 

    Puig Sadurní, Joaquim; Simó Torres, Carlos (2010-07)
    External research report
    Open Access
    Abstract. In this paper we investigate numerically the spectrum of some representative examples of discrete one-dimensional Schr¨odinger operators with quasi-periodic potential in terms of a perturbative constant b and ...
  • Resonance tongues in the quasi-periodic hill-Schrödinger equation with three frequencies 

    Puig Sadurní, Joaquim; Simó Torres, Carlos (2010-07)
    External research report
    Open Access
    In this paper we investigate numerically the following Hill’s equation x00 + (a + bq(t))x = 0 where q(t) = cos t + cosp2t + cosp3t is a quasiperiodic forcing with three rationally independent frequencies. It appears,also, as ...