Browsing by Author "Villanueva Castelltort, Jordi"

A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator
Borondo Rodríguez, Florentino; Luque Jiménez, Alejandro; Villanueva Castelltort, Jordi; Wisniacki, Diego Ariel (20091125)
Article
Restricted access  publisher's policyVortices 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 actionangle variables for elliptic lower dimensional tori
Luque Jiménez, Alejandro; Villanueva Castelltort, Jordi (201102)
Article
Restricted access  publisher's policyWe 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 actionangle variables for elliptic lower dimensional tori
Luque Jiménez, Alejandro; Villanueva Castelltort, Jordi (20100215)
External research report
Open AccessWe 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
Villanueva Castelltort, Jordi (20161018)
Article
Open AccessWe compute invariant Lagrangian tori of analytic Hamiltonian systems by the parameterization method. Under Kolmogorov’s nondegeneracy condition, we look for an invariant torus of the system carrying quasiperiodic motion ... 
A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map
Villanueva Castelltort, Jordi; Luque Jiménez, Alejandro (20160615)
Article
Open AccessWe present a numerical method for computing initial conditions of Lagrangian quasiperiodic 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
Villanueva Castelltort, Jordi (20180101)
Article
Open AccessWe 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
MartínezSeara Alonso, M. Teresa; Villanueva Castelltort, Jordi (1999)
Article
Open AccessIn 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
Fagella Rabionet, Núria; MartínezSeara Alonso, M. Teresa; Villanueva Castelltort, Jordi (2003)
Article
Open AccessIn this paper we consider the complexification of the Arnold standard family of circle maps given by $\widetilde F_{\alpha,\ep}(u)=u{\rm e}^{{\rm i}\alpha} {\rm e}^{\frac{\ep}{2}(u\frac{1}{u})}$, with $\alpha=\alpha( ... 
Confinement around the Vertical Family of Periodic Orbits close L<sub>4</sub> and L<sub>5</sub>
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (2001)
Article
Open AccessWe consider the spatial restricted three body problem (RTBP) for values of the mass parameter close to µRouth. We analyse the dynamics around the vertical periodic orbits which are born at the equilateral equilibrium ... 
Dynamics and bifurcation near the transition from stability to complex instability
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (2001)
Article
Open Access 
Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (1998)
Article
Open AccessWe consider a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet eigenvalues of opposite ... 
Dynamics close to a non semisimple 1: 1 resonant periodic orbit.
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (2003)
Article
Open AccessIn this work, our target is to analyze the dynamics around the $1:1$ resonance which appears when a family of periodic orbits of a real analytic threedegree of freedom Hamiltonian system changes its stability from ... 
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 ... 
KAM aspects of the quasiperiodic Hamiltonian Hopf bifurcation
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (2004)
Article
Open AccessIn this work we consider a normal form around a 1:1 non semisimple resonant periodic orbit of a threedegree of freedom Hamiltonian system. From the formal analysis it can be proved the branching off a twoparameter ... 
KAM aspects of the quasiperiodic Hamiltonian Hopf bifurcation: summary of results
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (s.n., 20070820)
Conference report
Open AccessIn this work we consider a 1:1 non semisimple resonant periodic orbit of a threedegrees of freedom real analytic Hamiltonian system. From the formal analysis of the normal form, it is proved the branching off a ... 
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 ... 
Kolmogorov Theorem Revisited
Villanueva Castelltort, Jordi (2004)
External research report
Open AccessKolmogorov 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 ... 
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 ... 
Motion close to the hopf bifurcation of the vertical family of periodic orbits of L^4
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón; Villanueva Castelltort, Jordi (2003)
Article
Open AccessThe paper deals with diﬀerent kinds of invariant motions (periodic orbits, 2D and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze the Hamiltonian direct Hopf bifurcation that takes place ...