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Dmitry Turaev

Professor in Dynamical Systems


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

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Dynamical Systems
Bifurcation Theory

Full list
Hamiltonian Dynamics
Homoclinic Tangencies


S.Gonchenko, D.Turaev, On three types of dynamics, and the notion of attractor, Proc. Steklov Inst. Math. 297, 116-137 (2017)

V.Gelfreich, D.Turaev, Arnold Diffusion in a priori chaotic symplectic maps, Comm. Math. Phys. 353, 507-547 (2017)

A.Gonchenko, S.Gonchenko, A.Kazakov, D.Turaev, On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators, Physica D 350, 45-57 (2017)

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)


M. Asaoka, K.Shinohara, D.Turaev, Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics, Math. Ann. 1-30 (2016)

D.Turaev, Averaging over a non-ergodic subsystem, "Anosov Systems and Modern Dynamics" abstracts book(2016)

D.Turaev, A.G.Vladimirov, S.Zelik, Interaction of spatial and temporal cavity solitons in mode-locked lasers and passive cavities, 2016 International Conference Laser Optics, IEEE (2016)

D.Turaev, Exponential energy growth due to slow parameter oscillations in quantum mechanical systems, Phys. Rev. E 93, 050203(R) (2016)

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)

K.Shah, V.Gelfreich, V.Rom-Kedar, D.Turaev, Leaky Fermi accelerators, Phys. Rev. E91, 062920 (2015)

T.Pereira, D.Turaev, Fast Fermi acceleration and entropy growth , Math. Model. Nat. Phenom. 10, 31-47 (2015)

D.Turaev, Maps close to identity and universal maps in the Newhouse domain , Comm. Math. Phys. 335, 1235-1277 (2015)

T.Pereira, D.Turaev, Exponential energy growth in adiabatically changing Hamiltonian systems, Phys. Rev. E91, 010901(R) (2015)


V.Gelfreich, V.Rom-Kedar, D.Turaev, Oscillating mushrooms: adiabatic theory for a non-ergodic system, J. Phys. A 47, 395101 (2014)

D.Turaev, Exponential Fermi acceleration in adiabatically perturbed Hamiltonian systems, Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014)

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)

D.Turaev, C.Warner, S.Zelik, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, Regul. Chaotic Dyn. 19, 513-522 (2014)

L.Shilnikov, A.Shilnikov, D.Turaev, Showcase of blue sky catastrophes, Bifurcation and Chaos 24, 1440003 (2014)

A.Gonchenko, S.Gonchenko, A.Kazakov, D.Turaev, Simple scenarios of onset of chaos in three-dimensional maps, Bifurcation and Chaos 24, 144005 (2014)

S.V.Gonchenko, J.S.W.Lamb, I.Rios, D.Turaev, Attractors and repellers near generic elliptic points of reversible maps, Doklady Math. 89, 65-67 (2014)


S.V.Gonchenko, A.S.Gonchenko, I.I.Ovsyannikov, D.Turaev, Examples of Lorenz-like attractors in Henon-like maps, Math. Model. Nat. Phenom. 8, 48-70 (2013)


D.Turaev, A.G.Vladimirov, S.Zelik, Long-range interaction and synchronization of oscillating dissipative solitons, Phys. Rev. Lett. 108, 263906 (2012)

V.Gelfreich, V.Rom-Kedar, D.Turaev, Fermi acceleration and adiabatic invariants for non-autonomous billiards, Chaos 22, 033116 (2012)

V.Rom-Kedar, D.Turaev, Billiards: A singular perturbation limit of smooth Hamiltonian flows, Chaos 22, 026102 (2012)

L.Lerman, D.Turaev, Breakdown of symmetry in reversible systems, Regul. Chaotic Dyn. 17, 318-336 (2012)

L.Lerman, D.Turaev, On bifurcations of symmetry loss in reversible systems, Rus. J. Nonlin. Dyn. 8, 323-343 (2012)

S.V.Gonchenko, I.I.Ovsyannikov, D.Turaev, On the effect of invisibility of stable periodic orbits at homoclinic bifurcations, Physica D 241, 1115-1122 (2012)


D.Turaev, On the splitting of invariant curves, Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)

V.Gelfreich, V.Rom-Kedar, K.Shah, D.Turaev, Robust exponential acceleration in time-dependent billiards, Phys. Rev. Lett. 106, 074101 (2011)

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

D.Turaev, Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness, Ergod. Th. & Dynam. Sys. 31, 563-569 (2011)

A.Vladimirov, D.Turaev, S.Zelik, Synchronization of interacting temporal cavity oscillons, in Proc. CLEO Europe - EQEC 2011 (IEEE Conference Publications, 2011)

M.Tlidi, A.Vladimirov, D.Turaev, Mobility properties of 2D cavity solitons in systems with delayed feedback, in Proc. CLEO Europe - EQEC 2011 (IEEE Conference Publications, 2011)


D.Turaev, Richness of chaos in the absolute Newhouse domain, in Proc. ICM 2010, vol.3 (Hindustan Book Agency, 2010) 1804-1815

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

K.Shah, D.Turaev, V.Rom-Kedar, Exponential energy growth in a Fermi accelerator, Phys. Rev. E 81, 056205 (2010)

V.Rom-Kedar , D.Turaev, The symmetric parabolic resonance, Nonlinearity 23, 1325-1351 (2010)

M.Tlidi, A.Vladimirov, D.Turaev, G.Kozyreff, D.Pieroux, T.Erneux, Spontaneous motion of localized structures and localized patterns induced by delayed feedback, Eur. Phys. J. D 59, 59-65 (2010)

V.Gelfreich, D.Turaev, Universal dynamics in a neighbourhood of a generic elliptic periodic point, Regul. Chaotic Dyn. 15,159-164 (2010)


M.Tlidi, A.Vladimirov, D.Pieroux, D.Turaev, Spontaneous motion of cavity solitons induced by a delayed feedback, Phys. Rev. Lett. 103, 103904 (2009)

S.V.Gonchenko, L.Shilnikov, D.Turaev, On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors, Regul. Chaotic Dyn. 14, 137-147 (2009)

D.Turaev, A.Vladimirov, S.Zelik, Strong enhancement of interaction of optical pulses induced by oscillatory instability, in Proc. CLEO Europe - EQEC 2009 (IEEE Conference Publications, 2009)


V.Gelfreich, D.Turaev, Fermi acceleration in non-autonomous billiards, J. Phys. A 41, 212003 (2008)

V.Gelfreich, D.Turaev, Unbounded energy growth in Hamiltonian systems with slowly varying parameter, Commun. Math. Phys. 283, 769-794 (2008)

D.Turaev, L.Shilnikov, Pseudohyperbolicity and the problem of periodic perturbation of Lorenz-like attractors, Doklady Math. 77 (2008)

S.V.Gonchenko, L.Shilnikov, D.Turaev, On dynamical properties of multidimensional diffeomorphisms from Newhouse regions: I, Nonlinearity 21 (2008)

D.Turaev, M.Radziunas, A.Vladimirov, Chaotic soliton walk in periodically modulated media, Phys. Rev. E 77(R) (2008)

A.Rapoport, V.Rom-Kedar, D.Turaev, Stability in high-dimensional steep repelling potentials, Commun. Math. Phys. 279 (2008)


S.V.Gonchenko, D.Turaev, L.Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps, Nonlinearity 20, 241-275 (2007)

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)

A.Rapoport, V.Rom-Kedar, D.Turaev, Approximating multi-dimensional Hamiltonian flows by billiards, Commun. Math. Phys. 272, 567-600 (2007)

A.Kirillov, D.Turaev, Foam-like structure of the Universe, Phys. Let. B 656, 1-8 (2007)

A.Shilnikov, D.Turaev, Blue-sky catastrophe, Scholarpedia 2(8):1889 (2007).


S.V.Gonchenko, K.Schneider, D.Turaev, Quasiperiodic regimes in multi-section semiconductor lasers, Regul. Chaotic Dyn. 11, 141-152 (2006)

A.Kirillov, D.Turaev, The Universal Rotation Curve of Spiral Galaxies, Mon. Not. Roy. Astron. Soc. 371, L31-L35 (2006)

S.V.Gonchenko, D.Turaev, L.Shilnikov, Homoclinic tangencies of arbitrarily high orders in conservative two-dimensional maps, Doclady Math. 73, 210-213 (2006)


S.V.Gonchenko, D.Turaev, L.Shilnikov, On dynamical properties of diffeomorphisms with homoclinic tangencies, J. Math. Sci. 126, 1317-1343 (2005)

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

A.Shilnikov, L.Shilnikov, D.Turaev, Blue-sky catastrophe in singularly perturbed systems, Moscow Math. J. 5, 205-218 (2005)

A.Vladimirov, D.Turaev, A new model for passive mode-locking in semiconductor lasers, Phys. Rev. A72, 033808, 1-13 (2005)

S.V.Gonchenko, I.I.Ovsyannikov, C.Simo, D.Turaev, Three-dimensional Henon-like map and wild Lorenz-like attractors, Bifurcation and Chaos 15, 3493-3508 (2005)

A.Shilnikov, L.Shilnikov, D.Turaev, Some mathematical problems of classical synchronization, in "Nonlinear waves'2004" (Nizhny Novgorod, 2005)

S.V.Gonchenko, L.P.Shilnikov, D.V.Turaev, On dynamical properties of diffeomorphisms with homoclinic tangencies, in Proc. Symposium Henrie Poincare, 41-72 (Solvay Inst., 2005)


A.Vladimirov, D.Turaev, G.Kozyreff, Delay differential equations for mode-locked semiconductor lasers, Opt. Lett. 29, 1221-1223 (2004)

A.Shilnikov, L.Shilnikov, D.Turaev, On some mathematical topics in classical synchronization, Bifurcation and Chaos 14, 2143-2160 (2004)

S.V.Gonchenko, D.V.Turaev, L.P.Shilnikov, Infinitely many elliptic periodic orbits in four-dimensional symplectic diffeomorphisms with a homoclinic tangency, Proc. Steklov Inst. Math. 244, 106-131 (2004)

A.Vladimirov, D.Turaev, A new model for a mode locked semiconductor laser, Radiophysics and Quantum Electronics 47, 769-776 (2004)


D.Turaev, Polynomial approximations of symplectic dynamics and richness of chaos in nonhyperbolic area-preserving maps, Nonlinearity 16, 1-13 (2003)

S.V.Gonchenko, L.P.Shilnikov, D.Turaev, On dynamical properties of diffeomorphisms with homoclinic tangencies, Sovrem. Mat. Prilozh. 7, 91-117 (2003)

A.Kirillov, D.Turaev, Corrections to the Newton and Coulomb potentials caused by effects of space-time foam, Gravitation and Cosmology 9, 267-269 (2003)

D.Turaev, V.Rom-Kedar, Soft billiards with corners, J. Stat. Phys. 112, 765-813 (2003)

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


J.Engländer, D.Turaev, A scaling limit theorem for a class of superdiffusions, Annals of Probability 30, 683-722 (2002)

A.Kirillov, D.Turaev, Modification of Newton's law of gravity at very large distances, Phys. Let. B 532, 185-192 (2002)

M.Wolfrum, D.Turaev, Instabilities of lasers with moderately delayed optical feedback, Opt. Com. 212, 127-138 (2002)


S.V.Gonchenko, D.Turaev, L.Shilnikov, Homoclinic tangencies of arbitrarily high orders in the Newhouse regions, J. Math. Sci 105, 1738-1778 (2001)

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)

L.Shilnikov, D.Turaev, A new simple bifurcation of a periodic orbit of blue sky catastrophe type, AMS Transl. Series II, v.200, 165-188 (2000)


S.V.Gonchenko, D.Turaev, L.P.Shilnikov, Homoclinic tangencies of arbitrarily high orders in the Newhouse regions, in Contemporary Mathematics and its Applications 67 (VINITI, Moscow, 1999)

V.N.Pisarevsky, A.Shilnikov, D.Turaev, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, Grazer Math. Berichte 339 (1999)

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

V.Rom-Kedar, D.Turaev, Big islands in dispersing billiard-like potentials, Physica D130, 187-210 (1999)


D.Turaev, V.Rom-Kedar, Elliptic islands appearing in near-ergodic flows, Nonlinearity 11, 575-599 (1998)

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

L.Bunimovich, D.Turaev, Localized solutions in lattice systems and their bifurcations caused by spatial interactions, Nonlinearity 11, 1539-1545 (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)

V.N.Pisarevsky, A.Shilnikov, D.Turaev, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, Regul. Chaotic Dyn. 2 (1998)

S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom, Regul. Chaotic Dyn. 3, 3-26 (1998)

D.Turaev, V.Rom-Kedar, On smooth Hamiltonian flows limiting to ergodic billiards, in "Chaos, kinetics and nonlinear dynamics in liquids and plasmas," Lect. Notes in Physics (1998)


L.P.Shilnikov, D.Turaev, On simple bifurcations leading to hyperbolic attractors, Comput. Math. Appl. 34, 441-457 (1997)

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)

S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Quasiattractors and homoclinic tangencies, Comput. Math. Appl. 34, 195-227 (1997)

S.V.Gonchenko, D.Turaev, L.P.Shilnikov, On Newhouse domains of two-dimensional diffeomorphisms with a structurally unstable heteroclinic cycle, Proc. Steklov Inst. Math. 216, 76-125 (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)

S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits, Chaos 6, 15-31 (1996)

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

S.V.Gonchenko, L.P.Shilnikov, D.Turaev, Bifurcations of two-dimensional diffeomorphisms with non-rough homoclinic contours, J. Techn. Phys. 37, 349-352 (1996)

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

S.V.Gonchenko, O.Sten'kin, D.Turaev, Complexity of homoclinic bifurcations and Ω-moduli , Bifurcation and Chaos 6, 969-989 (1996)

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


D.Turaev, L.P.Shilnikov, Blue sky catastrophes, Dokl. Math. 51, 404-407 (1995)


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

S.V.Gonchenko,L.P.Shilnikov, D.Turaev, On models with non-rough Poincare homoclinic curves , Physica D 62, 1-14 (1993)

S.V.Gonchenko, D.Turaev, L.P.Shilnikov, Dynamical phenomena in multi-dimensional systems with a structurally unstable Poincare homoclinic curve, Russian Acad. Sci., Dokl., Math. 47, 410-415 (1993)

S.V.Gonchenko, D.Turaev, L.P.Shilnikov, On the existence of Newhouse domains in a neighborhood of systems with a structurally unstable Poincare homoclinic curve (the higher-dimensional case), Russian Acad. Sci., Dokl., Math. 47, 268-273 (1993)


D.Turaev, Yu.Komlev, A.S.Dmitriev, Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol - Duffing equation, Bifurcation and Chaos 2, 93-100 (1992)

S.V.Gonchenko, D.Turaev, L.P.Shilnikov, On models with a structurally unstable Poincare homoclinic curve, Sov. Math., Dokl. 44, 422-426 (1992)


S.V.Gonchenko, D.Turaev, L.P.Shilnikov, On models with non-rough Poincare homoclinic curves, Methods of qualitative theory and theory of bifurcations, 36-61 (1991)


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.Biragov, I.M.Ovsyannikov, D.Turaev, A study of one endomorphism of a plane, Methods of qualitative theory and theory of bifurcations, 72-86 (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, L.P.Shilnikov, Bifurcations of quasiattractors torus-chaos, in "Mathematical mechanisms of turbulence," 113-121 (Kiev, 1986)


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)