ProfessorDmitryTuraev

Gonchenko SV, Shilnikov LP, Turaev DV, 1998, Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom, Regular and Chaotic Dynamics, Vol: 3, Pages: 3-26, ISSN: 1560-3547

We study bifurcations leading to the appearance of elliptic orbits in the case of four-dimensional symplectic diffeomorphisms (and Hamiltonian flows with three degrees of freedom) with a homoclinic tangency to a saddle-focus periodic orbit. © Regular and Chaotic Dynamics.

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• Citations: 12

Pisarevskii V, Shilnikov A, Turaev D, 1998, Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with symmetry, Regular and Chaotic Dynamics, Vol: 3, Pages: 19-27, ISSN: 1560-3547

Asymptotic normal forms for equilibria with a triplet of zero characteristic exponents in systems with ℤq-symmetry are listed. © Regular and Chaotic Dynamics.

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• Citations: 7

Turaev DV, Shi'nikov LP, 1998, An example of a wild strange attractor, Sbornik Mathematics, Vol: 189, Pages: 291-314, ISSN: 1064-5616

It is proved that in the space of Cr-smooth (r ≥ 4) flows in ℝn (n ≥ 4) there exist regions filled by systems that each have an attractor (here: a completely stable chain-transitive closed invariant set) containing a non-trivial basic hyperbolic set together with its unstable manifold, which has points of non-transversal intersection with the stable manifold. A construction is given for such a wild attractor containing an equilibrium state of saddle-focus type.

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• Citations: 74

Fiedler B, Turaev D, 1998, Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, Vol: 145, Pages: 129-159, ISSN: 0003-9527

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• Citations: 19

Leonid PShilnikov, Andrey L Shilnikov, Dmitry VTuraev, Leon O Chuaet al., 1998, Methods of Qualitative Theory in Nonlinear Dynamics. Part I, Publisher: World Scientific

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Gonchenko SV, Turaev DV, Gaspard P, Nicolis Get al., 1997, Complexity in the bifurcation structure of homoclinic loops to a saddle-focus, NONLINEARITY, Vol: 10, Pages: 409-423, ISSN: 0951-7715

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• Citations: 47

Gonchenko SV, Shilnikov LP, Turaev DV, 1997, Quasiattractors and homoclinic tangencies, Workshop on Computational Tools for Complex Systems, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 195-227, ISSN: 0898-1221

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• Citations: 37

Gonchenko SV, ShilNikov LP, Stenkin OV, Turaev DVet al., 1997, Bifurcations of systems with structurally unstable homoclinic orbits and moduli of Omega-equivalence, Workshop on Computational Tools for Complex Systems, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 111-142, ISSN: 0898-1221

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• Citations: 5

Shilnikov LP, Turaev DV, 1997, Simple bifurcations leading to hyperbolic attractors, Workshop on Computational Tools for Complex Systems, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 173-193, ISSN: 0898-1221

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• Citations: 27

Gonchenko SV, Stenkin OV, Turaev DV, 1996, Complexity of homoclinic bifurcations and Omega-moduli, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 6, Pages: 969-989, ISSN: 0218-1274

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• Citations: 10

Fiedler B, Turaev D, 1996, Coalescence of reversible homoclinic orbits causes elliptic resonance, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 6, Pages: 1007-1027, ISSN: 0218-1274

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• Citations: 11

Turaev D, 1996, On dimension of non-local bifurcational problems, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 6, Pages: 919-948, ISSN: 0218-1274

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• Citations: 38

Shashkov MV, Turaev DV, 1996, On the complex bifurcation set for a system with simple dynamics, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 6, Pages: 949-968, ISSN: 0218-1274

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• Citations: 10

Gonchenko SV, Shilnikov LP, Turaev DV, 1996, Dynamical phenomena in systems with structurally unstable Poincare homoclinic orbits, CHAOS, Vol: 6, Pages: 15-31, ISSN: 1054-1500

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• Citations: 84

TURAEV DV, SHILNIKOV LP, 1995, ON BLUE SKY CATASTROPHES, DOKLADY AKADEMII NAUK, Vol: 342, Pages: 596-599, ISSN: 0869-5652

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• Citations: 19

Shil'nikov AL, Shil'nikov LP, Turaev DV, 1993, NORMAL FORMS AND LORENZ ATTRACTORS, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 3, Pages: 1123-1139, ISSN: 0218-1274

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• Citations: 81

GONCHENKO SV, TURAEV DV, SHILNIKOV LP, 1993, DYNAMICAL PHENOMENA IN MULTIDIMENSIONAL SYSTEMS WITH NON-ROUGH POINCARE HOMOCLINIC CURVE, DOKLADY AKADEMII NAUK, Vol: 330, Pages: 144-147, ISSN: 0869-5652

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• Citations: 26

GONCHENKO SV, TURAEV DV, SHILNIKOV LP, 1993, ON AN EXISTENCE OF NEWHOUSE REGIONS NEAR SYSTEMS WITH NON-ROUGH POINCARE HOMOCLINIC CURVE (MULTIDIMENSIONAL CASE), DOKLADY AKADEMII NAUK, Vol: 329, Pages: 404-407, ISSN: 0869-5652

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• Citations: 24

GONCHENKO SV, SHILNIKOV LP, TURAEV DV, 1993, ON MODELS WITH NON-ROUGH POINCARE HOMOCLINIC CURVES, NATO ADVANCED RESEARCH WORKSHOP ON HOMOCLINIC CHAOS, Pages: 1-14

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MILLIONSHCHIKOV VM, SERGEEV IN, AKHMETOV MU, ARTAMONOV IN, FEKLIN VG, ZERNOV AE, LAPTINSKII VN, SUSHKO VG, IVANOV AG, IZOBOV NA, GONCHENKO SV, SHILNIKOV LP, ROZET IG, SADOVSKII AP, NAZAROV VI, POPOVA SN, TONKOV EL, GONCHENKO SV, TURAEV DV, SHILNIKOV LPet al., 1992, SEMINAR ON THE QUALITATIVE THEORY OF DIFFERENTIAL-EQUATIONS AT MOSCOW-UNIVERSITY, DIFFERENTIAL EQUATIONS, Vol: 28, Pages: 1655-1672, ISSN: 0012-2661

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Dmitriev AS, Komlev UA, Turaev DV, 1992, BIFURCATION PHENOMENA IN THE 1:1 RESONANT HORN FOR THE FORCED VAN DER POL-DUFFING EQUATION, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 2, Pages: 93-100, ISSN: 0218-1274

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• Citations: 10

TURAEV DV, SHILNIKOV LP, 1989, ON THE HAMILTONIAN-SYSTEMS WITH HOMOCLINIC CURVES FOR A SADDLE, DOKLADY AKADEMII NAUK SSSR, Vol: 304, Pages: 811-814, ISSN: 0002-3264

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• Citations: 18

ELEONSKII VM, KULAGIN NE, TURAEV DV, SHILNIKOV LPet al., 1989, ON THE CLASSIFICATION OF SELF-LOCALIZED STATES OF ELECTROMAGNETIC-FIELD IN NONLINEAR MEDIA, DOKLADY AKADEMII NAUK SSSR, Vol: 309, Pages: 848-852, ISSN: 0002-3264

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• Citations: 3

TURAEV DV, SHILNIKOV LP, 1986, BIFURCATIONS OF HOMOCLINIC 8 FOR A SADDLE WITH A NEGATIVE SADDLE VALUE, DOKLADY AKADEMII NAUK SSSR, Vol: 290, Pages: 1301-1304, ISSN: 0002-3264

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• Citations: 4