Now showing items 1-19 of 19

  • A new approach to the vakonomic mechanics 

    Llibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia Guennadievna (2014-11-01)
    Article
    Restricted access - publisher's policy
    The aim of this paper was to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider ...
  • Bi-asymptotic billiard orbits inside perturbed ellipsoids 

    Bolotin, S.; Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2001)
    Article
    Open Access
  • Effective reducibility of quasiperiodic linear equations close to constant coefficients 

    Jorba, Angel; Ramírez Ros, Rafael; Villanueva Castelltort, Jordi (1995)
    Article
    Open Access
    Let us consider the differential equation $$ \dot{x}=(A+\varepsilon Q(t,\varepsilon))x, \;\;\;\; |\varepsilon|\le\varepsilon_0, $$ where $A$ is an elliptic constant matrix and $Q$ depends on time in a quasiperiodic ...
  • Exponentially small asymptotic formulas for the length spectrum in some billiard tables 

    Martín, P.; Ramírez Ros, Rafael; Tamarit Sariol, A. (2016-04-05)
    Article
    Open Access
    Let q = 3 be a period. There are at least two (1, q)-periodic trajectories inside any smooth strictly convex billiard table. We quantify the chaotic dynamics of axisymmetric billiard tables close to their boundaries by ...
  • Exponentially small splitting of separatrices for perturbed integrable standard-like maps 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
    Article
    Open Access
    We consider fast quasiperiodic perturbations with two frequencies $(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum, where $\gamma$ is the golden mean number. The complete system has a two-dimensional invariant ...
  • Homoclinic billiard orbits inside symmetrically perturbed ellipsoids 

    Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2000)
    Article
    Open Access
    The billiard motion inside an ellipsoid of ${\bf R}^{3}$ is completely integrable. If the ellipsoid is not of revolution, there are many orbits bi-asymptotic to its major axis. The set of bi-asymptotic orbits is described ...
  • Homoclinic orbits of twist maps and billiards 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
    Article
    Open Access
    The splitting of separatrices for hyperbolic fixed points of twist maps with $d$ degrees of freedom is studied through a real-valued function, called the Melnikov potential. Its non-degenerate critical points are associated ...
  • Melnikov potential for exact symplectic maps 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
    Article
    Open Access
    The splitting of separatrices of hyperbolic fixed points for exact symplectic maps of $n$ degrees of freedom is considered. The non-degenerate critical points of a real-valued function (called the Melnikov potential) are ...
  • On Birkhoff's conjecture about convex billiards 

    Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1995)
    Article
    Open Access
    Birkhoff conjectured that the elliptic billiard was the only integrable convex billiard. Here we prove a local version of this conjecture: any non-trivial symmetric entire perturbation of an elliptic billiard is non-integrable.
  • On the length and area spectrum of analytic convex domains 

    Martín, Pau; Ramírez Ros, Rafael; Tamarit Sariol, A. (2016-01)
    Article
    Open Access
    Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for ...
  • 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
    Restricted access - publisher's policy
    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 ...