56 citations · 288 across the 14 of their papers we have counts for
6 papers · 1 filter
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…
Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
A. Delshams, M. S. Gonchenko, S. V. Gonchenko +1
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric n…
Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points
S. V. Gonchenko, I. I. Ovsyannikov, J. C. Tatjer
It was established in 2006 that bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a saddle-focus fixed point with the Jacobian equal to 1 can lead to…
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…
On bifurcations of area-preserving and non-orientable maps with quadratic homoclinic tangencies
Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfa…
On dynamics and bifurcations of area-preserving maps with homoclinic tangencies
Amadeu Delshams, Marina Gonchenko, Sergey Gonchenko
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfo…