40 citations · 127 across the 23 of their papers we have counts for
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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…
Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic…
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…
On dynamics and bifurcations of area-preserving maps with homoclinic tangencies
Amadeu Delshams, Marina Gonchenko, Sergey Gonchenko
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfo…
Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum.…