18 citations · 52 across the 11 of their papers we have counts for
12 papers
On 1:3 resonance under reversible perturbations of conservative cubic Hénon maps
M. S. Gonchenko, A. O. Kazakov, E. A. Samylina +1
We consider reversible non-conservative perturbations of the conservative cubic Hénon maps and study their influence on t…
Reversible perturbations of conservative Hénon-like maps
M. S. Gonchenko, S. V. Gonchenko, K. Safonov
For area-preserving Hénon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For c…
Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a p…
Exponentially small splitting of separatrices near a period-doubling bifurcation in area-preserving maps
Denis Gaidashev, Marina Gonchenko
We consider the conservative Hénon family at the period-doubling bifurcation of its fixed point and demonstrate that the separatrices of the fixed saddle point nearing the bifurcat…
Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps
Marina Gonchenko, Sergey V. Gonchenko, Ivan Ovsyannikov
We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different firs…
Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is…