Now showing items 1-20 of 29

  • 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 ...
  • EQUACIONS DIFERENCIALS 1 ( 1r Q ) 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2011-01-19)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS 1 ( 1r Q ) 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2010-11-04)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2011-01-19)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2014-01-07)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2013-11-07)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2013-01-14)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2012-01-12)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2011-10-28)
    Exam
    Restricted access to the UPC academic community
  • EQUACIONS DIFERENCIALS ORDINÀRIES 

    Ramírez Ros, Rafael (Universitat Politècnica de Catalunya, 2010-11-04)
    Exam
    Restricted access to the UPC academic community
  • 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 ...
  • Modelització amb sistemes d'EDOs lineals 

    Ramírez Ros, Rafael (2019-04-10)
    Audiovisual
    Open Access
  • 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 ...