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PROFESSOR DMITRY TURAEV

Dmitry Turaev

Professor in Dynamical Systems

 
 

Phone: +44(207)59-48566
Room: 634 Huxley Building

Home Page

TEACHING
Dynamical Systems
Bifurcation Theory

PUBLICATIONS
Full list
Hamiltonian Dynamics
Homoclinic Tangencies

M.Capinski, D.Turaev, P.Zgliczynski, Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system, Nonlinearity 31, 5410-5440 (2018)

D.Li, D.Turaev, Existence of heterodimensional cycles near Shilnikov loops in systems with a Z2 symmetry, DCDS 37, 4399-4437 (2017)

I.I.Ovsyannikov, D.Turaev, Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model, Nonlinearity 30, 115-137 (2017)

W.Giles, J.S.W.Lamb, D.Turaev, On homoclinic orbits to center manifolds of elliptic-hyperbolic equilibria in Hamiltonian systems, Nonlinearity 29, 3148-3173 (2016)

I.I.Ovsyannikov, D.Turaev, S.Zelik, Bifurcation to Chaos in the complex Ginzburg-Landau equation with large third-order dispersion, Modeling and Analysis of Information Systems 22, 327-336 (2015)

D.Turaev, Hyperbolic sets near homoclinic loops to a saddle for systems with a first integral, Regul. Chaotic Dyn. 19, 681-693 (2014)

V.S.Afraimovich, S.V.Gonchenko, L.Lerman, A.Shilnikov, D.Turaev, Scientific heritage of L.P.Shilnikov, Regul. Chaotic Dyn. 19, 435-460 (2014)

G.Tigan, D.Turaev, Analytical search for homoclinic bifurcations in Morioka-Shimizu model, Physica D 240, 985-989 (2011)

D.Turaev, S.Zelik, Analytical proof of space-time chaos in Ginzburg-Landau equations, DCDS-A 28, 1713-1751 (2010)

D.Turaev, A.Vladimirov, S.Zelik, Chaotic bound states of localized structures in the complex Ginzburg-Landau equation, Phys. Rev. E 75(R), 045601 (2007)

D.Turaev, An example of a resonant homoclinic loop of infinite cyclicity, Moscow Math. J. 5, 219-229 (2005)

D.Turaev, S. Zelik, Homoclinic bifurcations and dimension of the attractors for damped nonlinear hyperbolic equations, Nonlinearity 16, 1-36 (2003)

D.Turaev, Multi-pulse homoclinic loops in systems with a smooth first integral, in "Ergodic theory, analysis, and efficient simulation of dynamical systems" (Springer-Verlag, 2001)

M.Shashkov, D.Turaev, A proof of Shilnikov theorem for C1-smooth dynamical systems, AMS Transl. Series II, v.200, 149-163 (2000)

M.Shashkov, D.Turaev, An existence theorem for a nonlocal invariant manifold near a homoclinic loop, J. Non. Sci. 9, 1-49 (1999)

D.Turaev, L.P.Shilnikov, An example of a wild strange attractor, Sb. Math. 189, 137-160 (1998)

B.Fiedler, D.Turaev, Normal forms, resonances and meandering tip motions near relative equilibria of Euclidian group actions, Archive Rational Mech. Anal. 145, 129-159 (1998)

P.Gaspard, S.Gonchenko, G.Nicolis, D.Turaev, Complexity in the bifurcation structure of homoclinic loops to a saddle-focus, Nonlinearity 10, 409-423 (1997)

L.P.Shilnikov, D.Turaev, Super-homoclinic orbits and multi-pulse homoclinic loops in Hamiltonian systems with discrete symmetries, Regul. Chaotic Dyn. 2, 126-138 (1997)

S.V.Gonchenko, L.P.Shilnikov, O.Sten'kin, D.Turaev, Dynamical systems with structurally unstable homoclinic orbits and moduli of Ω-equivalence, Comput. Math. Appl. 34 (1997)

D.Turaev, On dimension of non-local bifurcational problems, Bifurcation and Chaos 6, 919-948 (1996)

D.Turaev, On dimension reduction near homoclinic and heteroclinic cycles, J. Techn. Phys. 37, 374-377 (1996)

M.Shashkov, D.Turaev, On the complex bifurcation set for a system with simple dynamics, Bifurcation and Chaos 6, 949-968 (1996)

B.Fiedler, D.Turaev, Coalescence of reversible homoclinics causes elliptic resonances , Bifurcation and Chaos 6, 1007-1027 (1996)

A.Shilnikov, L.P.Shilnikov, D.Turaev, Normal forms and Lorenz attractors, Bifurcation and Chaos 3, 1011-1037 (1993)

D.Turaev, L.P.Shilnikov, On Hamiltonian systems with homoclinic saddle curves, Sov. Math. Dokl. 39, 165-168 (1989)

V.M.Eleonsky, N.E.Kulagin, D.Turaev, L.P.Shilnikov, Classification of self-localized states of electromagnetic field within nonlinear medium, Soviet Phys. Doklady 34 (1989)

V.M.Eleonsky, N.E.Kulagin, D.Turaev, L.P.Shilnikov, On the classification of self-localized states of an electromagnetic field in a nonlinear medium, in "Nonlinear World," 235-238 (Naukova Dumka, 1989)

D.Turaev, On bifurcations of a homoclinic "figure eight" of a multi-dimensional saddle , Russ. Math. Surv. 43, 264-265 (1988)

D.Turaev, L.P.Shilnikov, On Hamiltonian systems with homoclinic curves of a saddle, in "Nonlinear and turbulent processes in physics," 148-151 (Naukova Dumka, 1988)

V.M.Eleonsky, N.E.Kulagin, D.Turaev, L.P.Shilnikov, On the classification of self-localized states of the electromagnetic field within nonlinear medium, Methods of qualitative theory and theory of bifurcations, 32-45 (1988)

D.Turaev, L.P.Shilnikov, On bifurcations of the homoclinic "figure eight" for a saddle with a negative saddle value, Sov. Math., Dokl. 34, 397-401 (1987)

D.Turaev, Bifurcations of two-dimensional dynamical systems close to a system with two separatrix loops , Russ. Math. Surv. 40, 243-244 (1985)

D.Turaev, One case of bifurcations of a contour composed by two homoclinic curves of a saddle, Methods of qualitative theory of differential equations, 45-58 (1984)

D.Turaev, Bifurcations of two-dimensional dynamical systems close to a system with two separatrix loops, Proc. XXIId Conference "Student and the Scientific Progress." Mathematics (Novosibirsk, 1984)