55 citations · 148 across the 7 of their papers we have counts for
7 papers
On Shilnikov attractors of three-dimensional flows and maps
Yuliya Bakhanova, Sergey Gonchenko, Alexander Gonchenko +2
We describe scenarios for the emergence of Shilnikov attractors, i.e. strange attractors containing a saddle-focus with two-dimensional unstable manifold, in the case of three-dime…
On discrete pseudohyperbolic attractors of Lorenz type
Sergey Gonchenko, Alexander Gonchenko, Alexey Kazakov
We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors, that can be observed in three-dimensional diffeomorphisms. We propose new phenomenol…
Elements of contemporary mathematical theory of dynamical chaos. Part 1. Pseudohyperbolic attractors
S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov +1
The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimen…
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…
Lorenz-like attractors in nonholonomic models of Celtic stone
A. S. Gonchenko, S. V. Gonchenko
We study chaotic dynamics in nonholonomic model of Celtic stone. We show that, for certain values of parameters characterizing geometrical and physical properties of the stone, a s…
Simple scenarios of onset of chaos in three-dimensional maps
Alexander Gonchenko, Sergey Gonchenko, Alexey Kazakov +1
We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to…