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math.DS2020
Reversible perturbations of conservative Hénon-like maps
M. S. Gonchenko, S. V. Gonchenko, K. Safonov
For area-preserving Hénon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For c…
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…