56 citations · 288 across the 14 of their papers we have counts for
15 papers
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…
On three types of dynamics, and the notion of attractor
Sergey Gonchenko, Dmitry Turaev
We propose a theoretical framework for an explanation of the numerically discovered phenomenon of the attractor-repeller merger. We identify regimes which are observed in dynamical…
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…
On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators
Alexander S. Gonchenko, Sergey V. Gonchenko, Alexey O. Kazakov +1
A one-parameter family of time-reversible systems on is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect bu…
Variety of strange pseudohyperbolic attractors in three-dimensional generalized H'enon maps
Alexander Gonchenko, Sergey Gonchenko
In the present paper we focus on the problem of the existence of strange pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange attr…
Homoclinic tangencies to resonant saddles and discrete Lorenz attractors
S. V. Gonchenko, I. I. Ovsyannikov
We study bifurcations of periodic orbits in three parameter general unfoldings of certain types quadratic homoclinic tangencies to saddle fixed points. We apply the rescaling techn…