Now showing items 1-20 of 27

• A numerical method for computing unstable quasi-periodic solutions for the 2-D Poiseuille flow ﻿

(1999)
Article
Open Access
• Dynamics and mission design near libration points, advanced methods for collinear points ﻿

(2000)
Article
Open Access
• Dynamics and mission design near libration points, advanced methods for triangular points ﻿

(2000)
Article
Open Access
The final objective of this work is to understand, analyze and compute the kinds of motion that appear on a vicinity (may be a large vicinity) of the geometrically defined equilateral points of the Earth-Moon system, as a ...
• 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 ...
• 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 ...
• Effective stability for periodically perturbed hamiltonian systems ﻿

(1994)
Article
Open Access
In this work we present a method to bound the diffusion near an elliptic equilibrium point of a periodically time-dependent Hamiltonian system. The method is based on the computation of the normal form (up to a certain ...
• Exponentially small splitting of separatrices under fast quasiperiodic forcing ﻿

(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 ...
• Invariant curves near Hamiltonian-Hopf bifurcations of 4D symplectic maps ﻿

(2003)
Article
Open Access
In this paper we give a numerical description of the neighbourhood of a fixed point of a symplectic map undergoing a transition from linear stability to complex instability, i.e., the so called Hamiltonian-Hopf bifurcation. ...
• 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 ...
• A la recerca de l'estabilitat efectiva dels asteroids trojans : algunes idees constructives de tècniques KAM sense ssar coordenades acció-angle ﻿

(2000)
Conference report
Open Access
Xerrada pel Seminari de Sistemes Dinamics UB-UPC. Barcelona, dimecres 19 de gener de 2000. Els trojans son una familia d'asteroids amb orbites situades no molt lluny del punt $L_5$ del sistema Sol-Jupiter. Si integrem ...
• Lindstedt series for lower dimensional tori ﻿

(1995)
Article
Open Access
We consider the existence and effective computation of low-dimensional (less independent frequencies than degrees of freedom) invariant tori of a near-integrable system. Lindstedt method is a systematic procedure to compute ...
• Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing ﻿

(1997)
Article
Open Access
Quasiperiodic perturbations with two frequencies $(1/\varepsilon ,\gamma /\varepsilon )$ of a pendulum are considered, where $\gamma$ is the golden mean number. We study the splitting of the three-dimensional invariant ...
• Nonlinear dynamics in an extended neighbourhood of the translunar equilibrium point ﻿

(1995)
Article
Open Access
• Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach ﻿

(2003)
Article
Open Access
We perform a bifurcation analysis of normal–internal resonances in parametrised families of quasi–periodically forced Hamiltonian oscillators, for small forcing. The unforced system is a one degree of freedom oscillator, ...
• Numerical computation of normal forms around some periodic orbits of the restricted three body problem ﻿

(1997)
Article
Open Access
In this paper we introduce a general methodology for computing (numerically) the normal form around a periodic orbit of an autonomous analytic Hamiltonian system. The process follows two steps. First, we expand the ...
• On quasiperiodic perturbations of elliptic equilibrium points ﻿

(1995)
Article
Open Access
This work focusses on quasiperiodic time-dependent perturbations of ordinary differential equations near elliptic equilibrium points. This means studying  \dot{x}=(A+\varepsilon Q(t,\varepsilon))x+\varepsilon ...
• On the normal behaviour of partially elliptic lower dimensional tori of hamiltonian systems ﻿

(1996)
Article
Open Access
The purpose of this paper is to study the dynamics near a reducible lower dimensional invariant tori of a finite-dimensional autonomous Hamiltonian system with $\ell$ degrees of freedom. We will focus in the case in ...
• On the persistence of lower dimensional invariant tori under quasiperiodic perturbations ﻿

(1996)
Article
Open Access
In this work we consider time dependent quasiperiodic perturbations of autonomous Hamiltonian systems. We focus on the effect that this kind of perturbations has on lower dimensional invariant tori. Our results show that, ...
• On the vertical families of two-dimensional tori near the triangular points of the bicircular problem ﻿

(1999)
Article
Open Access
This paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the Earth-Moon system. The model for the motion of the particle is the so-called Bicircular problem (BCP), that ...
• Quasi-periodic response solutions at normal-internal resonances ﻿

(2003)
Article
Open Access
In the conservative dynamics of certain quasi-periodically forced oscillators, normal-internal resonances are considered in a bifurcational setting. The unforced system is a one degree of freedom oscillator, under forcing ...