46 citations · 254 across the 37 of their papers we have counts for
41 papers
Soliton interaction and bound state formation in coupled Kerr resonators
Daria A. Dolinina, Dmitry V. Turaev, Andrei G. Vladimirov
Soliton dynamics in coupled Kerr microcavities is an important aspect of frequency comb technologies, with applications in optical communication and precision metrology. We investi…
Chaotic behavior in diffusively coupled systems
Eddie Nijholt, Tiago Pereira, Fernando C. Queiroz +1
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a…
Horseshoes for a class of nonuniformly expanding random dynamical systems on the circle
Jeroen S. W. Lamb, Giuseppe Tenaglia, Dmitry Turaev
We propose a notion of random horseshoe for one-dimensional random dynamical systems. We prove the abundance of random horseshoes for a class of circle endomorphisms subject to add…
Smooth Persistence of Attractors for Set-Valued Dynamical Systems: A Boundary Map Approach
K. Kourliouros, J. S. W. Lamb, M. Rasmussen +3
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamic…
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…