Publications
144 results found
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.
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.
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.
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, et al., 1998, Methods of Qualitative Theory in Nonlinear Dynamics. Part I, Publisher: World Scientific
Gonchenko SV, Turaev DV, Gaspard P, et 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, et 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
MILLIONSHCHIKOV VM, SERGEEV IN, AKHMETOV MU, et al., 1992, SEMINAR ON THE QUALITATIVE THEORY OF DIFFERENTIAL-EQUATIONS AT MOSCOW-UNIVERSITY, DIFFERENTIAL EQUATIONS, Vol: 28, Pages: 1655-1672, ISSN: 0012-2661
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, et 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
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