3 papers
math.DS2014
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…
math.DS2012
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…
math.DS2010
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…