Browsing by Author "Delshams Valdés, Amadeu"
Now showing items 1-20 of 88
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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>
(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.
(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
(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 of diffusion: rigorous verification in a priori unstable Hamiltonian systems
(2011-03-01)
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
(2010-07)
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
(2014-07)
Research report
Open Access -
A pseudo-normal form for planar vector fields
(2001)
Article
Open Access -
Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
(2013-01-01)
Article
Open AccessWe study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle fixed points. We consider one-parameter families of reversible maps unfolding ... -
Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
(2012-01-12)
Research report
Open AccessAbstract. We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible ... -
An invitation to singular symplectic geometry
(2017)
Research report
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bm- symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ... -
An invitation to singular symplectic geometry
(2019)
Article
Open AccessIn this paper we analyze in detail a collection of motivating examples to consider bm-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every bm-symplectic ... -
Arnold diffusion for a complete family of perturbations
(Springer, 2017-01-01)
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
(American Institute of Mathematical Sciences, 2018-12-01)
Article
Open AccessWe prove that for any non-trivial 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 diffusion for an a priori unstable Hamiltonian system with 3+1/2 degrees of freedom
(Institute of Physics (IOP), 2024-06-01)
Article
Open AccessIn the present paper, we apply the geometrical mechanism of diffusion in an a priori unstable Hamiltonian system [L. Chierchia and G. Gallavotti, Ann. l’I.H.P. Phys. théor. 60, 1–144 (1994)] with 3 + 1/2 degrees of freedom. ... -
Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument
(2016-11-01)
Article
Open AccessWe consider the spatial circular restricted three-body problem, on the motion of an infinitesimal body under the gravity of Sun and Earth. This can be described by a 3-degree of freedom Hamiltonian system. We fix an energy ... -
Bi-asymptotic billiard orbits inside perturbed ellipsoids
(2001)
Article
Open Access -
Consideracions al voltant de la Funció Beta a l’obra de Leonhard Euler (1707-1783)
(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
(2014-09)
Research report
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 consider ... -
Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
(Springer, 2014-11)
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 ... -
Correction to: exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
(2023-04)
Article
Open Access
