Now showing items 21-29 of 29

  • Persistence of homoclinic orbits for billiards and twist maps 

    Bolotin, S.; Delshams Valdés, Amadeu; Ramírez Ros, Rafael (2003)
    Article
    Open Access
    We consider the billiard motion inside a C2-small perturbation of a ndimensional ellipsoid Q with a unique major axis. The diameter of the ellipsoid Q is a hyperbolic two-periodic trajectory whose stable and unstable ...
  • Poincaré-Melnikov-Arnold method for analytic planar maps 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1995)
    Article
    Open Access
    The Poincare-Melnikov-Arnold method for planar maps gives rise to a Melnikov function defined by an infinite and (a priori) analytically uncomputable sum. Under an assumption of meromorphicity, residues theory can be ...
  • Poincaré-Melnikov-Arnold method for twist maps 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
    Article
    Open Access
    The Poincar\'e--Melnikov--Arnold method is the standard tool for detecting splitting of invariant manifolds for systems of ordinary differential equations close to ``integrable'' ones with associated separatrices. This ...
  • Singular separatrix splitting and Melnikov method: An experimental study 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1998)
    Article
    Open Access
    We consider families of analytic area-preserving maps depending on two pa- rameters: the perturbation strength E and the characteristic exponent h of the origin. For E=0, these maps are integrable with a separatrix to ...
  • Singular separatrix splitting and the Poincare-Melnikov method for area preserving maps 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1999)
    Article
    Open Access
    The splitting of separatrices of area preserving maps close to the identity is one of the most paradigmatic examples of an exponentially small or singular phenomenon. The intrinsic small parameter is the characteristic ...
  • Singular splitting of separatrices for the perturbed McMillan map 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1998)
    Article
    Open Access
  • Splitting of separatrices in Hamiltonian systems and symplectic maps 

    Delshams Valdés, Amadeu; Martínez-Seara Alonso, M. Teresa; Ramírez Ros, Rafael (1997)
    Article
    Open Access
    Poincar\'e, Melnikov and Arnol'd introduced the standard method for measuring the splitting of separatrices of Hamiltonian systems. It is based on the study of the zeros of the so-called Melnikov integral, a vectorial ...
  • Stability of the phase motion in race-track microtrons 

    Kubyshin, Yu A.; Larreal Barreto, Oswaldo; Ramírez Ros, Rafael; Martínez-Seara Alonso, M. Teresa (2017-06-15)
    Article
    Open Access
    We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. ...
  • The frequency map for billiards inside ellipsoids 

    Ramírez Ros, Rafael; Sánchez Casas, José Pablo (2010-04)
    External research report
    Open Access
    The billiard motion inside an ellipsoid Q Rn+1 is completely integrable. Its phase space is a symplectic manifold of dimension 2n, which is mostly foliated with Liouville tori of dimension n. The motion on each Liouville ...