Now showing items 1-20 of 30

• #### A new approach to the vakonomic mechanics ﻿

(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 ...
• #### Aprende cálculo con Youtube: con 333 problemas resueltos en Youtube ﻿

(Universitat Politècnica de Catalunya, 2021)
Problem statement, exercise
Open Access
• #### Bi-asymptotic billiard orbits inside perturbed ellipsoids ﻿

(2001)
Article
Open Access
• #### Effective reducibility of quasiperiodic linear equations close to constant coefficients ﻿

(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 ) ﻿

(Universitat Politècnica de Catalunya, 2010-11-04)
Exam
• #### EQUACIONS DIFERENCIALS 1 ( 1r Q ) ﻿

(Universitat Politècnica de Catalunya, 2011-01-19)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2014-01-07)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2013-01-14)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2013-11-07)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2012-01-12)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2011-01-19)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2011-10-28)
Exam
• #### EQUACIONS DIFERENCIALS ORDINÀRIES ﻿

(Universitat Politècnica de Catalunya, 2010-11-04)
Exam
• #### Exponentially small asymptotic formulas for the length spectrum in some billiard tables ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(2019-04-10)
Audiovisual
Open Access
• #### On Birkhoff's conjecture about convex billiards ﻿

(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.