4 citations · 10 across the 6 of their papers we have counts for
7 papers
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…
Leonid Shilnikov and mathematical theory of dynamical chaos
Alexey Kazakov, Sergey Gonchenko, Dmitry Turaev +1
This Focus Issue Global Bifurcations, Chaos, and Hyperchaos Theory and Applications is dedicated to the 85th anniversary of the great mathematician, one of the founding fathers of…
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…