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math.DS2023
On bifurcations of symmetric elliptic orbits
M. S. Gonchenko
We study bifurcations of symmetric elliptic fixed points in the case of \emph{p}:\emph{q} resonances with odd . We consider the case where the initial area-preserving map…
math.DS2014★ 4 cited
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…
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…