Now showing items 1-20 of 47

    • A characterization of isochronous centres in terms of symmetries 

      Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni (2000)
      Article
      Open Access
      We present a description of isochronous centres of planar vector fields $X$ by means of their groups of symmetries. More precisely, given a normalizer $U$ of $X$ (i.e., $[X,U]=\mu X$, where $\mu$ is a scalar function), we ...
    • A dynamic Parrondo's paradox for continuous seasonal systems 

      Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2019-11-27)
      External research report
      Open Access
      We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo's dynamic paradox, in which the stability of an equilibrium, common to all seasons is ...
    • A dynamic Parrondo's paradox for continuous seasonal systems 

      Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor (2020-04-29)
      Article
      Restricted access - publisher's policy
      We show that planar continuous alternating systems, which can be used to model systems with seasonality, can exhibit a type of Parrondo’s dynamic paradox, in which the stability of an equilibrium, common to all seasons is ...
    • An analytic-numerical method of computation of the Liapunov and period constants derived from their algebraic structure 

      Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1996)
      Article
      Open Access
      We consider the problem of computing the Liapunov and the period constants for a smooth differential equation with a non degenerate critical point. First, we investigate the structure of both constants when they are ...
    • An explicit expression of the first Liapunov and period constants with applications 

      Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1996)
      Article
      Open Access
      In this paper, we study systems in the plane having a critical point with pure imaginary eigenvalues, and we search for effective conditions to discern whether this critical point is a focus or a center; in the case of it ...
    • 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 (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 ...
    • 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 ...
    • Centre and isochronicity conditions for systems with homogeneous nonlinearities 

      Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor (1995)
      Article
      Open Access
      We study the centre-focus problem for systems with homogeneous nonlinearities. In the centre case we study the characterization of the isochronous centres. More explicitly, we derive six necessary conditions to be a ...
    • Continua of periodic points for planar integrable rational maps 

      Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor (Research India Publications, 2016-09)
      Article
      Open Access
      We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used by other authors and apply ...
    • Continua of periodic points for planar integrable rational maps. 

      Gasull Embid, Armengol; Llorens, Mireia; Mañosa Fernández, Víctor (2015-11-30)
      External research report
      Open Access
      We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals. The first two have been already used for other authors and apply ...
    • 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 (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 ...
    • 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 ...
    • 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 ...