Now showing items 1-6 of 6

  • Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma 

    Fontich i Julià, Ernest; Martín de la Torre, Pablo (2000)
    Article
    Open Access
    We consider differentiable maps having an invariant torus with normal behavior having a central part. We prove the existence and regularity of pseudostable manifolds and regularity with respect to parameters. Then we ...
  • 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
    Restricted access - publisher's policy
    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
    Restricted access - publisher's policy
    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 in the perturbed McMillan map 

    Martínez-Seara Alonso, M. Teresa; Martín de la Torre, Pablo; Sauzin, D. (2009-12)
    External research report
    Open Access
    The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. ...
  • Hamiltonian systems with orbits covering densely submanifolds of small codimension 

    Fontich i Julià, Ernest; Martín de la Torre, Pablo (2000)
    Article
    Open Access
    The existence of a transition chain in a Hamiltonian system leads to the existence of orbits shadowing it, if some lambda lemma can be applied. This fact has been used to prove the existence of diffusion in perturbations ...
  • Resurgence of inner solutions for perturbations of the McMillan map 

    Martínez-Seara Alonso, M. Teresa; Sauzin, D.; Martín de la Torre, Pablo (2009-12)
    External research report
    Open Access
    A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove ...