Now showing items 1-20 of 21

  • Basin of attraction of triangular maps with applications 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2013-07-25)
    External research report
    Open Access
    We consider some planar triangular maps. These maps preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction ...
  • Basin of attraction of triangular maps with applications 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2014-03)
    Article
    Open Access
    We consider planar triangular maps that preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of ...
  • Bifurcation of 2-periodic orbits from non-hyperbolic fixed points 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2017-07-21)
    External research report
    Open Access
    We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful ...
  • Bifurcation of 2-periodic orbits from non-hyperbolic fixed points 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2018-01)
    Article
    Open Access
    We introduce the concept of 2-cyclicity for families of one-dimensional maps with a non-hyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful ...
  • Different approaches to the global periodicity problem 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor; Mañosas, Francesc (2013-07-25)
    External research report
    Open Access
    t Let F be a real or complex n-dimensional map. It is said that F is globally periodic if there exists some p ∈ N + such that Fp(x) = x for all x, where F k = F ◦ F k−1, k ≥ 2. The minimal p satisfying this property is ...
  • Global periodicity conditions for maps and recurrences via Normal Forms 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2012-05-04)
    Other
    Open Access
    We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions ...
  • Global periodicity conditions for maps and recurrences via normal forms 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2013-11)
    Article
    Open Access
    We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of K, where K is ℝ or ℂ, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary ...
  • Integrability and non-integrability of periodic non-autonomous Lyness recurrences 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2013-12-01)
    Article
    Open Access
    This paper studies non-autonomous Lyness-type recurrences of the form x n+2 = (a n + x n+1)/x n , where {a n } is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k {1, 2, 3, ...
  • Integrability and non-integrability of periodic non-autonomous Lyness recurrences 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2010-12-22)
    Other
    Open Access
    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 ...
  • Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version) 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2011-12-22)
    Other
    Open Access
    This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the ...
  • Non autonomous 2-periodic Gumovski-Mira difference equations 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2011-06-01)
    External research report
    Open Access
    We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ...
  • Non-autonomous two periodic Gumovski-Mira difference equations 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2012-12)
    Article
    Open Access
    We consider two types of nonautonomous two-periodic Gumovski–Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the two-periodic ...
  • Non-integrability of measure preserving maps via Lie symmetries 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2015-03-18)
    External research report
    Open Access
    We consider the problem of characterizing, for certain natural number m, the local C^m-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability ...
  • Non-integrability of measure preserving maps via Lie symmetries 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2015-11-15)
    Article
    Open Access
    We consider the problem of characterizing, for certain natural number m, the local C^m-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability ...
  • 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 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 ...
  • Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2017-01-20)
    Working paper
    Open Access
    We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the ...
  • Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2018-02)
    Article
    Open Access
    We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for ...
  • Periodic points, Lie symmetries and non-integrability of planar maps 

    Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2017-07-03)
    Lecture
    Open Access