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PROFESSOR DMITRY TURAEV
Professor in Dynamical Systems
Phone: +44(207)59-48566
Room: 634 Huxley Building
TEACHING
PUBLICATIONS
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D.Turaev,
Maps close to identity and universal maps in the Newhouse domain , Comm. Math. Phys. 335, 1235-1277 (2015)
D.Turaev, Richness of chaos in the absolute Newhouse domain, in Proc. ICM 2010, vol.3 (Hindustan Book Agency, 2010) 1804-1815
D.Turaev, On dimension of non-local bifurcational problems, Bifurcation and Chaos 6, 919-948 (1996)
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)
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)
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D.Turaev, Diffeomorphisms which cannot be topologically conjugate to diffeomorphisms of a higher smoothness, Ergod. Th. & Dynam. Sys. 31, 563-569 (2011) |
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D.Turaev, Polynomial approximations of symplectic dynamics and richness of chaos in nonhyperbolic area-preserving maps, Nonlinearity 16, 1-13 (2003) |
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V.Gelfreich, D.Turaev, Universal dynamics in a neighbourhood of a generic elliptic periodic point, Regul. Chaotic Dyn. 15,159-164 (2010) |
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P.Berger,
D.Turaev,
On Herman's positive entropy conjecture, Advances in Mathematics 349, 1234-1288 (2019)
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S.V.Gonchenko, L.P.Shilnikov, D.Turaev, On models with non-rough Poincare homoclinic curves, Physica D 62, 1-14 (1993)
            
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Russian version: On models with non-rough Poincare homoclinic curves, Methods of qualitative theory and theory of bifurcations, 36-61 (1991) |
Short version: |
On models with a structurally unstable Poincare homoclinic curve, Sov. Math., Dokl. 44, 422-426 (1992)
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Detailed proofs: |
Homoclinic tangencies of arbitrarily high orders in the Newhouse regions, J. Math. Sci 105, 1738-1778 (2001) |
            
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Russian version: Homoclinic tangencies of arbitrarily high orders in the Newhouse regions, in Contemporary Mathematics and its Applications 67 (VINITI, Moscow, 1999) | |
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S.V.Gonchenko, O.Sten'kin, D.Turaev, Complexity of homoclinic bifurcations and Ω-moduli , Bifurcation and Chaos 6, 969-989 (1996) |
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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) | |
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Conference proceedings: 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) |
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, L.Shilnikov, D.Turaev, On dynamical properties of multidimensional
diffeomorphisms from Newhouse regions: I, Nonlinearity 21 (2008)
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)
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) |
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) | |
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Wild attractors
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, L.Shilnikov, Pseudohyperbolicity and the problem of periodic perturbation of Lorenz-like attractors, Doklady Math. 77 (2008)
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)
D.Turaev, L.P.Shilnikov, An example of a wild strange attractor, Sb. Math. 189, 137-160 (1998)
Examples
D.Turaev, V.Rom-Kedar, Elliptic islands appearing in near-ergodic flows, Nonlinearity 11, 575-599 (1998)
A.Dmitriev, Yu.Komlev, D.Turaev, Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol - Duffing equation, Bifurcation and Chaos 2, 93-100 (1992)
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)
D.Turaev, L.P.Shilnikov, Bifurcations of quasiattractors torus-chaos, in "Mathematical mechanisms of turbulence," 113-121 (Kiev, 1986)
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