3 citations · 6 across the 4 of their papers we have counts for
5 papers · 1 filter
Universal bifurcation patterns in the unfolding of a pair of homoclinic tangencies
Sergey Gonchenko, Dongchen Li, Dmitry Turaev
We study generic two- and three-parameter unfoldings of a pair of orbits of quadratic homoclinic tangency in strongly dissipative systems. We prove that the corresponding stability…
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…
Wild pseudohyperbolic attractor in a four-dimensional Lorenz system
Sergey Gonchenko, Alexey Kazakov, Dmitry Turaev
We present an example of a new strange attractor which, as we show, belongs to a class of wild pseudohyperbolic spiral attractors. We find this attractor in a four-dimensional syst…
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…