46 citations · 254 across the 37 of their papers we have counts for
5 papers · 1 filter
Persistent heterodimensional cycles in periodic perturbations of Lorenz-like attractors
Dongchen Li, Dmitry Turaev
We prove that heterodimensional cycles can be created by unfolding a pair of homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This implies the existence of a…
Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system
Maciej J. Capinski, Dmitry Turaev, Piotr Zgliczynski
We prove, by employing rigorous numerics, that Shimizu-Morioka system has a Lorenz attractor for an open set of parameter values. Using this result, we prove the existence of a dis…
Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse
Carl P. Dettmann, Vitaly Fain, Dmitry Turaev
We study billiard dynamics inside an ellipse for which the axes lengths are changed periodically in time and an -small quartic polynomial deformation is added to the boundary…
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…
Equilibration of energy in slow-fast systems
Kushal Shah, Dmitry Turaev, Vassili Gelfreich +1
Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. On the other hand, it is known that in slow-fast systems ergodicity of t…