Ara es mostren els items 1-19 de 19

• A new approach to the vakonomic mechanics ﻿

(2014-11-01)
Article
Accés restringit per política de l'editorial
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 ...

(2001)
Article
Accés obert
• Effective reducibility of quasiperiodic linear equations close to constant coefficients ﻿

(1995)
Article
Accés obert
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 ﻿

(2016-04-05)
Article
Accés obert
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 ﻿

(1997)
Article
Accés obert
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 ﻿

(2000)
Article
Accés obert
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 ﻿

(1997)
Article
Accés obert
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 ﻿

(1997)
Article
Accés obert
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 ﻿

(1995)
Article
Accés obert
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 ﻿

(2016-01)
Article
Accés obert
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 ﻿

(2003)
Article
Accés obert
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 ﻿

(1995)
Article
Accés obert
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 ﻿

(1997)
Article
Accés obert
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 ﻿

(1998)
Article
Accés obert
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 ﻿

(1999)
Article
Accés obert
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 ...

(1998)
Article
Accés obert
• Splitting of separatrices in Hamiltonian systems and symplectic maps ﻿

(1997)
Article
Accés obert
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 ﻿

(2017-06-15)
Article
Accés restringit per política de l'editorial
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 ﻿

(2010-04)
Report de recerca
Accés obert
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 ...