• Bifurcations analysis of oscillating hypercycles 

    Guillamon Grabolosa, Antoni; Fontich, Ernest; Sardañés, Josep (2015-12-21)
    Article
    Accés obert
    We investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n > 4) the existence of a stable periodic orbit has been previously ...
  • Dynamical systems on lattices with decaying interaction I: A functional analysis framework 

    Fontich, Ernest; Llave Canosa, Rafael de la; Martín de la Torre, Pablo (2011-03-15)
    Article
    Accés restringit per política de l'editorial
    We consider weakly coupled map lattices with a decaying interaction. That is, we consider systems which consist of a phase space at every site such that the dynamics at a site is little affected by the dynamics at far ...
  • Dynamical systems on lattices with decaying interaction II: Hyperbolic sets and their invariant manifolds 

    Fontich, Ernest; Llave Canosa, Rafael de la; Martín de la Torre, Pablo (2011-03-15)
    Article
    Accés restringit per política de l'editorial
    This is the second part of the work devoted to the study of maps with decay in lattices. Here we apply the general theory developed in Fontich et al. (2011) to the study of hyperbolic sets. In particular, we establish that ...
  • Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results 

    Baldomá Barraca, Inmaculada; Fontich, Ernest; Guàrdia Munarriz, Marcel; Martínez-Seara Alonso, M. Teresa (2011)
    Report de recerca
    Accés obert
    In this paper we study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation which is fast and periodic in time. We provide ...
  • Full analysis of small hypercycles with shortcircuits in prebiotic evolution 

    Lázaro Ochoa, José Tomás; Guillamon Grabolosa, Antoni; Fontich, Ernest; Sardañés, Josep (2017-01-05)
    Article
    Accés restringit per política de l'editorial
    It is known that hypercycles are sensitive to the so-called parasites and short-circuits. While the impact of parasites has been widely investigated for well-mixed and spatial hypercycles, the effect of short-circuits in ...
  • Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points 

    Baldomá Barraca, Inmaculada; Fontich, Ernest; Martín, Pau (2017-08-01)
    Article
    Accés obert
    We study the Gevrey character of a natural parameterization of one dimensional invariant manifolds associated to a parabolic direction of fixed points of analytic maps, that is, a direction associated with an eigenvalue ...