Browsing by Author "Jorba, Angel"

A numerical method for computing unstable quasiperiodic solutions for the 2D Poiseuille flow
Sánchez Casas, José Pablo; Jorba, Angel (1999)
Article
Open Access 
Dynamics and mission design near libration points, advanced methods for collinear points
Gómez, Gerard; Jorba, Angel; Masdemont Soler, Josep; Simó Torres, Carlos (2000)
Article
Open AccessPreface and table of contents of a forthcoming book published by World Scientific 
Dynamics and mission design near libration points, advanced methods for triangular points
Gómez, Gerard; Jorba, Angel; Masdemont Soler, Josep; Simó Torres, Carlos (2000)
Article
Open AccessThe 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 EarthMoon system, as a ... 
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 ... 
Effective Stability Around Periodic Orbits of the Spatial RTBP
Jorba, Angel; Villanueva Castelltort, Jordi (1995)
Article
Open AccessIn 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
Jorba, Angel; Simó Torres, Carlos (1994)
Article
Open AccessIn this work we present a method to bound the diffusion near an elliptic equilibrium point of a periodically timedependent 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
Delshams Valdés, Amadeu; Gelfreich, Vassili; Jorba, Angel; MartínezSeara Alonso, M. Teresa (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 ... 
Invariant curves near HamiltonianHopf bifurcations of 4D symplectic maps
Jorba, Angel; Ollé Torner, Mercè (2003)
Article
Open AccessIn 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 HamiltonianHopf bifurcation. ... 
KAM Theory without actionangle variables
González, Alejandra; Jorba, Angel; Llave Canosa, Rafael de la; Villanueva Castelltort, Jordi (2003)
Article
Open AccessGiven 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 actionangle ... 
A la recerca de l'estabilitat efectiva dels asteroids trojans : algunes idees constructives de tècniques KAM sense ssar coordenades accióangle
Jorba, Angel; Llave Canosa, Rafael de la; Villanueva Castelltort, Jordi (2000)
Conference report
Open AccessXerrada pel Seminari de Sistemes Dinamics UBUPC. 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 SolJupiter. Si integrem ... 
Lindstedt series for lower dimensional tori
Jorba, Angel; Llave Canosa, Rafael de la; Zou, Maorong (1995)
Article
Open AccessWe consider the existence and effective computation of lowdimensional (less independent frequencies than degrees of freedom) invariant tori of a nearintegrable 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
Delshams Valdés, Amadeu; Gelfreich, Vassili; Jorba, Angel; MartínezSeara Alonso, M. Teresa (1997)
Article
Open AccessQuasiperiodic 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 threedimensional invariant ... 
Nonlinear dynamics in an extended neighbourhood of the translunar equilibrium point
Jorba, Angel; Masdemont Soler, Josep (1995)
Article
Open Access 
Normalinternal resonances in quasiperiodically forced oscillators: a conservative approach
Broer, H. W.; Hanssmann, Heinz; Jorba, Angel; Villanueva Castelltort, Jordi; Wagener, Florian (2003)
Article
Open AccessWe 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
Jorba, Angel; Villanueva Castelltort, Jordi (1997)
Article
Open AccessIn 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
Jorba, Angel; Simó Torres, Carlos (1995)
Article
Open AccessThis work focusses on quasiperiodic timedependent 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
Jorba, Angel; Villanueva Castelltort, Jordi (1996)
Article
Open AccessThe purpose of this paper is to study the dynamics near a reducible lower dimensional invariant tori of a finitedimensional 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
Jorba, Angel; Villanueva Castelltort, Jordi (1996)
Article
Open AccessIn 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 twodimensional tori near the triangular points of the bicircular problem
Castella Carlos, Enric; Jorba, Angel (1999)
Article
Open AccessThis paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the EarthMoon system. The model for the motion of the particle is the socalled Bicircular problem (BCP), that ... 
Quasiperiodic response solutions at normalinternal resonances
Broer, H. W.; Hanssmann, Heinz; Jorba, Angel; Villanueva Castelltort, Jordi; Wagener, Florian (2003)
Article
Open AccessIn the conservative dynamics of certain quasiperiodically forced oscillators, normalinternal resonances are considered in a bifurcational setting. The unforced system is a one degree of freedom oscillator, under forcing ...