Browsing by Author "Delshams Valdés, Amadeu"

Abundance of attracting, repelling and elliptic periodic orbits in twodimensional reversible maps
Delshams Valdés, Amadeu; Gonchenko, S.V.; Lázaro Ochoa, José Tomás; Stenkin, Oleg (20130101)
Article
Open AccessWe study dynamics and bifurcations of twodimensional reversible maps having nontransversal heteroclinic cycles containing symmetric saddle fixed points. We consider oneparameter families of reversible maps unfolding ... 
Abundance of attracting, repelling and elliptic periodic orbits in twodimensional reversible maps
Delshams Valdés, Amadeu; Lázaro Ochoa, José Tomás; Gonchenko, S.V.; Sten'kin, Oleg (20120112)
External research report
Open AccessAbstract. We study dynamics and bifurcations of twodimensional reversible maps having nontransversal heteroclinic cycles containing symmetric saddle periodic points. We consider oneparameter families of reversible ... 
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: 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 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 of diffusion: rigorous verification in a priori unstable Hamiltonian systems
Delshams Valdés, Amadeu; Huguet Casades, Gemma (20110301)
Article
Restricted access  publisher's policyIn this paper we consider a representative a priori unstable Hamiltonian system with 2 + 1/2 degrees of freedom and we apply the geometric mechanism for diffusion introduced in [A. Delshams, R. de la Llave, T.M. Seara, ... 
A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems
Delshams Valdés, Amadeu; Huguet Casades, Gemma (201007)
External research report
Open AccessIn this paper we consider a representative a priori unstable Hamiltonian system with 2 + 1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. ... 
A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (201407)
External research report
Open Access 
An invitation to singular symplectic geometry
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Dempsey Bradell, Roisin Mary; Oms, Cedric; Planas Bahí, Arnau (2019)
Article
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bmsymplectic forms and foldedtype symplectic structures. In particular, we provide models in Celestial Mechanics for every bmsymplectic ... 
An invitation to singular symplectic geometry
Miranda Galcerán, Eva; Delshams Valdés, Amadeu; Planas Bahí, Arnau; Oms, Cedric; Dempsey Bradell, Roisin Mary (2017)
External research report
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bm symplectic forms and foldedtype symplectic structures. In particular, we provide models in Celestial Mechanics for every bmsymplectic ... 
A pseudonormal form for planar vector fields
Delshams Valdés, Amadeu; Guillamon Grabolosa, Antoni; Lázaro Ochoa, José Tomás (2001)
Article
Open Access 
Arnold diffusion for a complete family of perturbations
Delshams Valdés, Amadeu; Gonçalves Schaefer, Rodrigo (Springer, 20170101)
Article
Open AccessIn this work we illustrate the Arnold diffusion in a concrete example — the a priori unstable Hamiltonian system of 2 + 1/2 degrees of freedom H(p, q, I, f, s) = p2/2+ cos q  1 + I2/2 + h(q, f, s; e) — proving that for ... 
Arnold diffusion for a complete family of perturbations with two independent harmonics
Delshams Valdés, Amadeu; Gonçalves Schaefer, Rodrigo (American Institute of Mathematical Sciences, 20181201)
Article
Open AccessWe prove that for any nontrivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete ... 
Arnold's mechanism of diffusion in the spatial circular restricted threebody problem: A semianalytical argument
Delshams Valdés, Amadeu; Gidea, Marian; Roldán, Pablo (20161101)
Article
Open AccessWe consider the spatial circular restricted threebody problem, on the motion of an infinitesimal body under the gravity of Sun and Earth. This can be described by a 3degree of freedom Hamiltonian system. We fix an energy ... 
Biasymptotic billiard orbits inside perturbed ellipsoids
Bolotin, S.; Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2001)
Article
Open Access 
Consideracions al voltant de la Funció Beta a l’obra de Leonhard Euler (17071783)
Delshams Valdés, Amadeu; Massa Esteve, Maria Rosa (Centre de recerca per a la Història de la Tècnica "Francesc Santponç i Roca". Escola Tècnica Superior d'Enginyeria Industrial de Barcelona (Universitat Politècnica de Catalunya). Càtedra UNESCO de Tècnica i Cultura de la UPC, 2008)
Article
Open Access 
Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (201409)
External research report
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearlyintegrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider ... 
Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (Springer, 201411)
Article
Open AccessWe study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We ... 
Effective stability and KAM theory
Delshams Valdés, Amadeu; Gutiérrez Serrés, Pere (1995)
Article
Open AccessThe two main stability results for nearly integrable Hamiltonian systems are revisited: Nekhoroshev theorem, concerning exponential lower bounds for the stability time (effective stability), and KAM theorem, concerning ... 
Effective stability in reversible systems
Delshams Valdés, Amadeu; Lázaro Ochoa, José Tomás (1997)
Article
Open AccessIn this paper we present a procedure to put in normal form a nearlyintegrable reversible system, not necessarily a Hamiltonian system. Furthermore, nonresonant stability estimates are obtained. As an application we discuss ...