Now showing items 1-20 of 35

• #### A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator ﻿

(2009-11-25)
Article
Restricted access - publisher's policy
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie–Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a ...
• #### A KAM theorem without action-angle variables for elliptic lower dimensional tori ﻿

(2011-02)
Article
Restricted access - publisher's policy
We study elliptic lower dimensional invariant tori of Hamiltonian systems via parametrizations. The method is based on solving iteratively the functional equations that stand for invariance and reducibility. In contrast ...
• #### A KAM theorem without action-angle variables for elliptic lower dimensional tori ﻿

(2010-02-15)
Research report
Open Access
We study elliptic lower dimensional invariant tori of Hamiltonian systems via parameterizations. The method is based in solving iteratively the functional equations that stand for invariance and reducibility. In contrast ...
• #### A new approach to the parameterization method for Lagrangian tori of hamiltonian systems ﻿

(2016-10-18)
Article
Open Access
We compute invariant Lagrangian tori of analytic Hamiltonian systems by the parameterization method. Under Kolmogorov’s non-degeneracy condition, we look for an invariant torus of the system carrying quasi-periodic motion ...
• #### A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map ﻿

(2016-06-15)
Article
Open Access
We present a numerical method for computing initial conditions of Lagrangian quasi-periodic invariant tori of Hamiltonian systems and symplectic maps. Such initial conditions are found by solving, using the Newton method, ...
• #### A parameterization method for Lagrangian tori of exact symplectic maps of R2r ﻿

(2018-01-01)
Article
Open Access
We are concerned with analytic exact symplectic maps of ${\mathbb R}^{2r}$ endowed with the standard symplectic form. We study the existence of a real analytic torus of dimension $r$, invariant by the map and carrying ...
• #### Asymptotic behaviour of the domain of analyticity of invariant curves of the standard map ﻿

(1999)
Article
Open Access
In this paper we consider the standard map, and we study the invariant curve obtained by analytical continuation, with respect to the perturbative parameter E, of the invariant circle of rotation number the golden mean ...
• #### Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery ﻿

(2003)
Article
Open Access
• #### Effective Stability Around Periodic Orbits of the Spatial RTBP ﻿

(1995)
Article
Open Access
In this work we study the dynamics around an elliptic periodic orbit of Hamiltonian systems. To this end we have developped an algorithm to compute a normal form (up to a finite order) around this orbit, that gives an ...
• #### FUNCIONS DE VARIABLE COMPLEXA | EXTRAORDINARI ﻿

(Universitat Politècnica de Catalunya, 2020-07-14)
Exam
• #### FUNCIONS DE VARIABLE COMPLEXA | FINAL ﻿

(Universitat Politècnica de Catalunya, 2020-06-12)
Exam
• #### KAM aspects of the quasi-periodic Hamiltonian Hopf bifurcation: summary of results ﻿

(s.n., 2007-08-20)
Conference report
Open Access
In this work we consider a 1:-1 non semi-simple resonant periodic orbit of a three-degrees of freedom real analytic Hamiltonian system. From the formal analysis of the normal form, it is proved the branching off a ...
• #### KAM aspects of the quasiperiodic Hamiltonian Hopf bifurcation ﻿

(2004)
Article
Open Access
In this work we consider a normal form around a 1:-1 non semi-simple resonant periodic orbit of a three-degree of freedom Hamiltonian system. From the formal analysis it can be proved the branching off a two-parameter ...
• #### KAM Theory without action--angle variables ﻿

(2003)
Article
Open Access
Given a torus approximately invariant under a symplectic map, we find sufficient conditions for the existence of a true invariant torus close to the given one. We do not assume either that we are working on action-angle ...
• #### Kolmogorov Theorem Revisited ﻿

(2004)
Research report
Open Access
Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required ...