Browsing by Author "Llave Canosa, Rafael de la"
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A general mechanism of diffusion in hamiltonian systems: qualitative results
Gidea, Marian; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (20190101)
Article
Open AccessWe present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach is based on following the “outer dynamics” along homoclinic orbits to a ... 
A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold
Gidea, Marian; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (2020)
Article
Open AccessWe describe a recent method to show instability in Hamiltonian systems. The main hypothesis of the method is that some explicit transversality conditions – which can be verified in concrete systems by finite calculations ... 
A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of T<sup>2</sup>
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (1999)
Article
Open AccessWe give a proof based in geometric perturbation theory of a result proved by J.N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a generic geodesic flow in T^2 ... 
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model.
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe introduce a geometric mechanism for di?usion in a priori unstable nearly integrable dynamical systems. It is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and ... 
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe present a geometric mechanism for diﬀusion in Hamiltonian systems. We also present tools that allow to verify it in a concrete model. In particular, we verify it in a system which presents the large gap problem. 
A smooth center manifold theorem which applies to some IIIposed partial differential equations with unbounded nonlinearities
Llave Canosa, Rafael de la (2009)
Article
Restricted access  publisher's policyWe prove the existence of a smooth center manifold for several partial differential equations, including ill posed equations with unbounded nonlinearities. We also prove smooth dependence on parameters with respect to ... 
Computation of limit cycles and their isochrons: Fast algorithms and their convergence
Huguet Casades, Gemma; Llave Canosa, Rafael de la (2013)
Article
Restricted access  publisher's policyWe present efficient algorithms to compute limit cycles and their isochrons (i.e., the sets of points with the same asymptotic phase) for planar vector fields. We formulate a functional equation for the parameterization ... 
Dynamical systems on lattices with decaying interaction I: A functional analysis framework
Fontich, Ernest; Llave Canosa, Rafael de la; Martín de la Torre, Pablo (20110315)
Article
Restricted access  publisher's policyWe consider weakly coupled map lattices with a decaying interaction. That is, we consider systems which consist of a phase space at every site such that the dynamics at a site is little affected by the dynamics at far ... 
Dynamical systems on lattices with decaying interaction II: Hyperbolic sets and their invariant manifolds
Fontich, Ernest; Llave Canosa, Rafael de la; Martín de la Torre, Pablo (20110315)
Article
Restricted access  publisher's policyThis is the second part of the work devoted to the study of maps with decay in lattices. Here we apply the general theory developed in Fontich et al. (2011) to the study of hyperbolic sets. In particular, we establish that ... 
Geometric properties of the scattering map of a normally hyperbolic invariant manifold
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; Seara, Tere M. (20061010)
Article
Open AccessGiven a normally hyperbolic invariant manifold $\Lambda$ for a map $f$, whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an ... 
Geometric properties of the scattering map of a normally hyperbolic invariant manifold
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; Seara, Tere M. (Elsevier, 2008)
Article
Open AccessGiven a normally hyperbolic invariant manifold Λ for a map f , whose stable and unstable invariant manifolds intersect transversally, we consider its associated scattering map. That is, the map that, given an asymptotic ... 
Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (20160514)
Article
Open AccessWe consider models given by Hamiltonians of the form View the MathML sourceH(I,f,p,q,t;e)=h(I)+¿j=1n±(12pj2+Vj(qj))+eQ(I,f,p,q,t;e) Turn MathJax on where I¿I¿Rd,f¿TdI¿I¿Rd,f¿Td, p,q¿Rnp,q¿Rn, t¿T1t¿T1. These are higher ... 
KAM theory and a partial justification of Greene's criterion for nontwist maps
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la (1999)
Article
Open AccessWe consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric ... 
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 ... 
Orbits of unbounded energy in quasiperiodic perturbations of geodesic flows
Delshams Valdés, Amadeu; Llave Canosa, Rafael de la; MartínezSeara Alonso, M. Teresa (2003)
Article
Open AccessWe show that certain mechanical systems, including a geodesic °ow in any dimension plus a quasiperiodic perturbation by a potential, have orbits of unbounded energy. The assumptions we make in the case of geodesic °ows ... 
Teoria Kam Sin Coordenadas AccionAngulo
González, Alejandra; Jorba, Angel; Llave Canosa, Rafael de la; Villanueva Castelltort, Jordi (2001)
Article
Open AccessThe classical KAM methods, strongly supported on the use of canonical trans formations in the actionangle context, are not effcient to be applied to a wide range of systems in which the Hamiltonian is known (for instance) ... 
The parameterization method for invariant manifolds I: manifolds associated to nonresonant subspaces
Cabré Vilagut, Xavier; Fontich i Julià, Ernest; Llave Canosa, Rafael de la (2002)
Article
Open AccessWe introduce a method to prove existence of invariant manifolds and, at the same time to find simple polynomial maps which are conjugated to the dynamics on them. As a first application, we consider the dynamical system ... 
The parameterization method for invariant manifolds II: regularity with respect to parameters
Cabré Vilagut, Xavier; Fontich i Julià, Ernest; Llave Canosa, Rafael de la (2002)
Article
Open AccessWe study the regularity with respect to parameters of the invariant manifolds associated to nonresonant subspaces obtained in the previous article [CFdlL00].