Now showing items 17-30 of 30

  • 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 ...
  • The period function for Hamiltonian systems with homogeneous nonlinearities 

    Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor; Mañosas Capellades, Francesc (1996)
    Article
    Open Access
    The paper deals with Hamiltonian systems with homogeneous nonlinearities. We prove that such systems have no isochronous centers, that the period annulus of any of its centres is either bounded or the whole plane and that ...
  • The period function for second-order quadratic ODEs is monotone 

    Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Villadelprat Yagüe, Jordi (2003)
    Article
    Open Access
    Very little is known about the period function for large families of centers. In one of the pioneering works on this problem, Chicone [?] conjectured that all the centers encountered in the family of second-order differential ...
  • Upper bounds for the number of zeroes for some Abelian integrals 

    Gasull Embid, Armengol; Lázaro Ochoa, José Tomás; Torregrosa, Joan (2012-09)
    Article
    Restricted access - publisher's policy
    Consider the vector field x′=−yG(x,y),y′=xG(x,y), where the set of critical points {G(x,y)=0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal directions. We perturb it ...
  • Upper bounds for the number of zeroes for some Abelian Integrals 

    Lázaro Ochoa, José Tomás; Gasull Embid, Armengol; Torregrosa, Joan (2012-01-12)
    External research report
    Open Access
    Abstract. Consider the vector field x0 = -yG(x, y), y0 = xG(x, y), where the set of critical points {G(x, y) = 0} is formed by K straight lines, not passing through the origin and parallel to one or two orthogonal ...