3 papers
math.DS2017
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…
math.DS2012
Attractors and repellers near generic elliptic points of reversible maps
Sergey Gonchenko, Jeroen Lamb, Isabel Rios +1
We show that resonance zones near an elliptic periodic point of a reversible map must, generically, contain asymptotically stable and asymptotically unstable periodic orbits, along…
nlin.CD2005
Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
S. V. Gonchenko, J. D. Meiss, I. I. Ovsyannikov
We study bifurcations of a three-dimensional diffeomorphism, , that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers $(λe^{i\vphi}, λe^{-i\vp…