46 citations · 254 across the 37 of their papers we have counts for
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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…
Generators of groups of Hamitonian maps
Pierre Berger, Dmitry Turaev
We prove that analytic Hamiltonian dynamics on tori, annuli, or Euclidean space can be approximated by a composition of nonlinear shear maps where each of the shears depends only o…
Stable motions of high energy particles interacting via a repelling potential
V. Rom-Kedar, D. Turaev
The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all suf…
Learning reversible symplectic dynamics
Riccardo Valperga, Kevin Webster, Victoria Klein +2
Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in m…
Robust heterodimensional cycles in two-parameter unfolding of homoclinic tangencies
Dongchen Li, Xiaolong Li, Katsutoshi Shinohara +1
We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for ($…
Control of the Schrödinger equation by slow deformations of the domain
Alessandro Duca, Romain Joly, Dmitry Turaev
The aim of this work is to study the controllability of the Schrödinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-Δu(t)~~~~~\text{ on }Ω(t) \tag{} \end{e…