19 citations · 23 across the 5 of their papers we have counts for
6 papers · 1 filter
Breakdown of homoclinic orbits to of the hydrogen atom in a circularly polarized microwave field
Amadeu Delshams, Mercè Ollé, Juan Ramon Pacha +1
We consider the Rydberg electron in a circularly polarized microwave field, whose dynamics is described by a 2 d.o.f. Hamiltonian, which is a perturbation of size of the stan…
Arnold diffusion for a complete family of perturbations
Amadeu Delshams, Rodrigo G. Schaefer
In this work we illustrate the Arnold diffusion in a concrete example---the \emph{a priori} unstable Hamiltonian system of degrees of freedom $H(p,q,I,φ,s) = p^{2}/2+\cos q…
On bifurcations of area-preserving and non-orientable maps with quadratic homoclinic tangencies
Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfa…
A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
The aim of this work is to provide asymptotic estimates for the splitting of separatrices in a perturbed 3-degree-of-freedom Hamiltonian system, associated to a 2-dimensional whisk…
Transition map and shadowing lemma for normally hyperbolic invariant manifolds
Amadeu Delshams, Marian Gidea, Pablo Roldan
For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories w…
A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems
Amadeu Delshams, Gemma Huguet
In 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…