Now showing items 7-26 of 30

  • 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 ...
  • First derivative of the period function with applications 

    Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2001)
    Article
    Open Access
    Given a centre of a planar differential system, we extend the use of the Lie bracket to the determination of the monotonicity character of the period function. As far as we know, there are no general methods to study ...
  • 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 ...
  • Identification of one-parameter bifurcations giving rise to periodic orbits, from their period function. 

    Gasull Embid, Armengol; Mañosa Fernández, Víctor; Villadelprat Yagüe, Jordi (Universitat Politècnica de Catalunya. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), 2009)
    Conference report
    Open Access
  • 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 

    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 (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 ...
  • Limit cycles and Lie symmetries 

    Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2005)
    Article
    Open Access
    Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem ...
  • Limit cycles for generalized Abel equations 

    Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2005)
    Article
    Open Access
    This paper deals with the problem of finding upper bounds on the number of periodic solutions of a class of one-dimensional non-autonomous differential equations: those with the right-hand sides being polynomials of ...
  • 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 ...
  • 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 the Chebyshev property for a new family of functions 

    Lázaro Ochoa, José Tomás; Gasull Embid, Armengol; Torregrosa, Joan (2012-03)
    Article
    Open Access
  • 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 ...
  • Period function for perturbed isochronous centres 

    Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2001)
    Article
    Open Access
  • Phase portrait of Hamiltonian systems with homogeneous nonlinearities 

    Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1999)
    Article
    Open Access
    The main goal of this work is to describe the phase portarit of Hamiltonian systems with a non degenerate center at the origin and homogeneous nonlinearities of arbitrary degree n. We apply our results to the case n=2 to ...
  • Rational periodic sequences for the Lyness recurrence 

    Gasull Embid, Armengol; Mañosa Fernández, Víctor; Xarles Ribas, Xavier (2010-04-30)
    Other
    Open Access
    Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with ...