Browsing by Author "Ramírez Ros, Rafael"

A new approach to the vakonomic mechanics
Llibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia Guennadievna (20141101)
Article
Restricted access  publisher's policyThe aim of this paper was to show that the Lagranged'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 ... 
Biasymptotic 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 AccessLet 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. (20160405)
Article
Open AccessLet 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 standardlike maps
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
Article
Open AccessWe 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 twodimensional invariant ... 
Homoclinic billiard orbits inside symmetrically perturbed ellipsoids
Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2000)
Article
Open AccessThe billiard motion inside an ellipsoid of ${\bf R}^{3}$ is completely integrable. If the ellipsoid is not of revolution, there are many orbits biasymptotic to its major axis. The set of biasymptotic orbits is described ... 
Homoclinic orbits of twist maps and billiards
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
Article
Open AccessThe splitting of separatrices for hyperbolic fixed points of twist maps with $d$ degrees of freedom is studied through a realvalued function, called the Melnikov potential. Its nondegenerate critical points are associated ... 
Melnikov potential for exact symplectic maps
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
Article
Open AccessThe splitting of separatrices of hyperbolic fixed points for exact symplectic maps of $n$ degrees of freedom is considered. The nondegenerate critical points of a realvalued function (called the Melnikov potential) are ... 
On Birkhoff's conjecture about convex billiards
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1995)
Article
Open AccessBirkhoff conjectured that the elliptic billiard was the only integrable convex billiard. Here we prove a local version of this conjecture: any nontrivial symmetric entire perturbation of an elliptic billiard is nonintegrable. 
On the length and area spectrum of analytic convex domains
Martín, Pau; Ramírez Ros, Rafael; Tamarit Sariol, A. (201601)
Article
Open AccessAreapreserving 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 AccessWe consider the billiard motion inside a C2small perturbation of a ndimensional ellipsoid Q with a unique major axis. The diameter of the ellipsoid Q is a hyperbolic twoperiodic trajectory whose stable and unstable ... 
PoincaréMelnikovArnold method for analytic planar maps
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1995)
Article
Open AccessThe PoincareMelnikovArnold 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 ... 
PoincaréMelnikovArnold method for twist maps
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1997)
Article
Open AccessThe Poincar\'eMelnikovArnold 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 AccessWe consider families of analytic areapreserving 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 PoincareMelnikov method for area preserving maps
Delshams Valdés, Amadeu; Ramírez Ros, Rafael (1999)
Article
Open AccessThe 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; MartínezSeara Alonso, M. Teresa; Ramírez Ros, Rafael (1997)
Article
Open AccessPoincar\'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 socalled Melnikov integral, a vectorial ... 
Stability of the phase motion in racetrack microtrons
Kubyshin, Yu A.; Larreal Barreto, Oswaldo; Ramírez Ros, Rafael; MartínezSeara Alonso, M. Teresa (20170615)
Article
Restricted access  publisher's policyWe model the phase oscillations of electrons in racetrack 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 (201004)
External research report
Open AccessThe 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 ...