메뉴 건너뛰기




Volumn 14, Issue 1, 2009, Pages 137-147

On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors

Author keywords

Homoclinic tangency; Lorenz attractor; Strange attractor; Wild hyperbolic attractor

Indexed keywords


EID: 60349108289     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1134/S1560354709010092     Document Type: Article
Times cited : (48)

References (32)
  • 1
    • 79955577320 scopus 로고
    • On Three-Dimensional Dynamical Systems Close to Systems with a Structurally Unstable Homoclinic Curve, Part I
    • Part II, Mat. Sb., 1973, vol. 19, pp. 139-156 (in Russian)
    • Gavrilov, N.K. and Shilnikov, L.P., On Three-Dimensional Dynamical Systems Close to Systems with a Structurally Unstable Homoclinic Curve, Part I, Mat. Sb., 1972, vol. 17, pp. 467-485; Part II, Mat. Sb., 1973, vol. 19, pp. 139-156 (in Russian).
    • (1972) Mat. Sb. , vol.17 , pp. 467-485
    • Gavrilov, N.K.1    Shilnikov, L.P.2
  • 2
    • 32044475236 scopus 로고
    • Diffeomorphisms with Infinitely Many Sinks
    • Newhouse, S.E., Diffeomorphisms with Infinitely Many Sinks, Topology, 1974, vol. 13, pp. 9-18.
    • (1974) Topology , vol.13 , pp. 9-18
    • Newhouse, S.E.1
  • 3
    • 0041801952 scopus 로고
    • On Stable Periodic Motions in Systems Close to a System with a Nontransversal Homoclinic Curve
    • [Math. Notes, 1983, vol. 33, pp. 384-389]
    • Gonchenko, S. V., On Stable Periodic Motions in Systems Close to a System with a Nontransversal Homoclinic Curve, Mat. Zametki, 1983, vol. 33, pp. 745-756 [Math. Notes, 1983, vol. 33, pp. 384-389].
    • (1983) Mat. Zametki , vol.33 , pp. 745-756
    • Gonchenko, S.V.1
  • 4
    • 0011271968 scopus 로고
    • Dynamical Phenomena in Multi-Dimensional Systems with a Non-Rough Poincaré Homoclinic Curve
    • Gonchenko, S. V., Turaev, D. V., and Shilnikov, L.P., Dynamical Phenomena in Multi-Dimensional Systems with a Non-Rough Poincaré Homoclinic Curve, Russ. Acad. Sci. Dokl. Math., 1993, vol. 47, pp. 410-415.
    • (1993) Russ. Acad. Sci. Dokl. Math. , vol.47 , pp. 410-415
    • Gonchenko, S.V.1    Turaev, D.V.2    Shilnikov, L.P.3
  • 5
    • 0039023464 scopus 로고
    • High Dimension Diffeomorphisms Displaying Infinitely Many Sinks
    • Palis, J. and Viana, M., High Dimension Diffeomorphisms Displaying Infinitely Many Sinks, Ann. Math., 1994, vol. 140, pp. 91-136.
    • (1994) Ann. Math. , vol.140 , pp. 91-136
    • Palis, J.1    Viana, M.2
  • 6
    • 43049144272 scopus 로고    scopus 로고
    • On Dynamical Properties of Multidimensional Diffeomorphisms from Newhouse Regions, I
    • Gonchenko, S.V., Shilnikov, L.P., and Turaev, D.V., On Dynamical Properties of Multidimensional Diffeomorphisms from Newhouse Regions, I, Nonlinearity, 2008, vol. 21, pp. 923-972.
    • (2008) Nonlinearity , vol.21 , pp. 923-972
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3
  • 7
    • 33644914312 scopus 로고    scopus 로고
    • On Bifurcations of the Birth of Closed Invariant Curves in the Case of Two-Dimensional Diffeomorphisms with Homoclinic Tangencies
    • Gonchenko, S.V. and Gonchenko, V. S., On Bifurcations of the Birth of Closed Invariant Curves in the Case of Two-Dimensional Diffeomorphisms with Homoclinic Tangencies, Proc. Steklov Inst. Math., 2004, vol. 244, pp. 80-105.
    • (2004) Proc. Steklov Inst. Math. , vol.244 , pp. 80-105
    • Gonchenko, S.V.1    Gonchenko, V.S.2
  • 8
    • 37349105501 scopus 로고    scopus 로고
    • Bifurcations of Three-Dimensional Diffeomorphisms with Non-Simple Quadratic Homoclinic Tangencies and Generalized Hénon Maps
    • Gonchenko, S. V., Gonchenko, V. S., and Tatjer, J. C., Bifurcations of Three-Dimensional Diffeomorphisms with Non-Simple Quadratic Homoclinic Tangencies and Generalized Hénon Maps, Regul. Chaotic Dyn., 2007, vol. 12, no. 3, pp. 233-266.
    • (2007) Regul. Chaotic Dyn. , vol.12 , Issue.3 , pp. 233-266
    • Gonchenko, S.V.1    Gonchenko, V.S.2    Tatjer, J.C.3
  • 9
    • 0005283382 scopus 로고    scopus 로고
    • Dynamical Phenomena in Systems with Structurally Unstable Poincaré Homoclinic Orbits
    • Gonchenko, S. V., Sten'kin O.V., and Shilnikov, L.P., Dynamical Phenomena in Systems with Structurally Unstable Poincaré Homoclinic Orbits, Chaos, 2006, vol. 6, pp. 15-31.
    • (2006) Chaos , vol.6 , pp. 15-31
    • Gonchenko, S.V.1    Sten'kin, O.V.2    Shilnikov, L.P.3
  • 10
    • 0242344635 scopus 로고
    • Abundance of Strange Attractors
    • Mora, L. and Viana, M., Abundance of Strange Attractors, Acta Math., 1993, vol. 171, no. 1, pp. 1-71.
    • (1993) Acta Math. , vol.171 , Issue.1 , pp. 1-71
    • Mora, L.1    Viana, M.2
  • 11
    • 0002768228 scopus 로고
    • Strange Attractors and Quasiattractors
    • in G.I. Barenblatt, G. Iooss, D.D. Joseph (Eds.), Boston: Pitmen
    • Aframovich, V. S. and Shilnikov, L.P., Strange Attractors and Quasiattractors, in Nonlinear Dynamics and Turbulence, G.I. Barenblatt, G. Iooss, D.D. Joseph (Eds.), Boston: Pitmen, 1983.
    • (1983) Nonlinear Dynamics and Turbulence
    • Aframovich, V.S.1    Shilnikov, L.P.2
  • 13
    • 0000119416 scopus 로고
    • On Attracting Structurally Unstable Limit Sets of Lorenz Attractor Type
    • Afraimovich, V. S., Bykov, V.V., and Shilnikov, L.P., On Attracting Structurally Unstable Limit Sets of Lorenz Attractor Type, Trans. Moscow Math. Soc., 1982, vol. 44, pp. 153-216.
    • (1982) Trans. Moscow Math. Soc. , vol.44 , pp. 153-216
    • Afraimovich, V.S.1    Bykov, V.V.2    Shilnikov, L.P.3
  • 14
    • 0009568318 scopus 로고
    • The Origin and Structure of the Lorenz Attractor
    • Afraimovich, V. S., Bykov, V.V., and Shilnikov, L.P., The Origin and Structure of the Lorenz Attractor, Dokl. Phys., 1977, vol. 22, pp. 253-255.
    • (1977) Dokl. Phys. , vol.22 , pp. 253-255
    • Afraimovich V.S. Bykov, V.V.1    Shilnikov, L.P.2
  • 15
    • 0032220873 scopus 로고    scopus 로고
    • An Example of a Wild Strange Attractor
    • Turaev, D.V. and Shilnikov, L.P., An Example of a Wild Strange Attractor, Mat. Sb., 1998, vol. 189, pp. 291-314.
    • (1998) Mat. Sb. , vol.189 , pp. 291-314
    • Turaev, D.V.1    Shilnikov, L.P.2
  • 16
    • 41549128876 scopus 로고    scopus 로고
    • Pseudo-Hyperbolicity and the Problem on Periodic Perturbations of Lorenz-like Attractors
    • Turaev, D.V. and Shilnikov, L.P., Pseudo-Hyperbolicity and the Problem on Periodic Perturbations of Lorenz-like Attractors, Russian Dokl. Math., 2008, vol. 77, no. 1, pp. 17-21.
    • (2008) Russian Dokl. Math. , vol.77 , Issue.1 , pp. 17-21
    • Turaev, D.V.1    Shilnikov, L.P.2
  • 18
    • 0011317754 scopus 로고
    • On Models with a Structurally Unstable Homoclinic Poincaré Curve
    • Gonchenko, S. V., Shilnikov, L.P., and Turaev, D. V., On Models with a Structurally Unstable Homoclinic Poincaré Curve, Soviet Math. Dokl., 1992, vol. 44, pp. 422-426.
    • (1992) Soviet Math. Dokl. , vol.44 , pp. 422-426
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3
  • 19
    • 0042871500 scopus 로고    scopus 로고
    • Homoclinic Tangencies of Any Order in Newhouse Regions
    • Gonchenko, S.V., Shilnikov, L.P., and Turaev, D.V., Homoclinic Tangencies of Any Order in Newhouse Regions, J. Math. Sci., 2001, vol. 105, pp. 1738-1778.
    • (2001) J. Math. Sci. , vol.105 , pp. 1738-1778
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3
  • 20
    • 33947622603 scopus 로고    scopus 로고
    • Homoclinic Tangencies of Arbitrarily High Orders in Conservative and Dissipative Two-Dimensional Maps
    • Gonchenko, S., Shilnikov, L., and Turaev, D., Homoclinic Tangencies of Arbitrarily High Orders in Conservative and Dissipative Two-Dimensional Maps, Nonlinearity, 2007, vol. 20, pp. 241-275.
    • (2007) Nonlinearity , vol.20 , pp. 241-275
    • Gonchenko, S.1    Shilnikov, L.2    Turaev, D.3
  • 21
    • 51249181043 scopus 로고
    • The Abundance of Wild Hyperbolic Sets and Non-Smooth Stable Sets for Diffeomorphisms
    • Newhouse, S.E., The Abundance of Wild Hyperbolic Sets and Non-Smooth Stable Sets for Diffeomorphisms, Publ. Math. Inst. Hautes Études Sci., 1979, vol. 50, pp. 101-151.
    • (1979) Publ. Math. Inst. Hautes Études Sci. , vol.50 , pp. 101-151
    • Newhouse, S.E.1
  • 23
    • 33745583790 scopus 로고    scopus 로고
    • Chaotic Dynamics of Three-Dimensional Hénon Maps that Originate from a Homoclinic Bifurcation
    • Gonchenko, S. V., Meiss, J. D., and Ovsyannikov, I. I., Chaotic Dynamics of Three-Dimensional Hénon Maps that Originate from a Homoclinic Bifurcation, Regul. Chaotic Dyn., 2006, vol. 11, pp. 191-212.
    • (2006) Regul. Chaotic Dyn. , vol.11 , pp. 191-212
    • Gonchenko, S.V.1    Meiss, J.D.2    Ovsyannikov, I.I.3
  • 24
    • 0002591468 scopus 로고
    • A Two-Dimensional Mapping with a Strange Attractor
    • Hénon, M., A Two-Dimensional Mapping with a Strange Attractor, Comm. Math. Phys., 1976, vol. 50, pp. 69-77.
    • (1976) Comm. Math. Phys. , vol.50 , pp. 69-77
    • Hénon, M.1
  • 25
    • 0040417832 scopus 로고
    • Bifurcation and Chaos in the Marioka-Shimizu System
    • in Gorky (in Russian) [Selecta Math. Soviet., 1991, vol. 10, pp. 105-117]
    • Shilnikov, A. L., Bifurcation and Chaos in the Marioka-Shimizu System, in Methods of Qualitative Theory of Differential Equations, Gorky, 1986, pp. 180-193 (in Russian) [Selecta Math. Soviet., 1991, vol. 10, pp. 105-117].
    • (1986) Methods of Qualitative Theory of Differential Equations , pp. 180-193
    • Shilnikov, A.L.1
  • 26
    • 0000764166 scopus 로고
    • On Bifurcations of the Lorenz Attractor in the Shimuizu-Morioka Model
    • Shilnikov, A. L., On Bifurcations of the Lorenz Attractor in the Shimuizu-Morioka Model, Physica D, 1993, vol. 62, pp. 338-346.
    • (1993) Physica D , vol.62 , pp. 338-346
    • Shilnikov, A.L.1
  • 27
    • 60349086322 scopus 로고    scopus 로고
    • On the Lorenz Attractor in the Shimuizu-Morioka Model
    • submitted to
    • Tigan, G. and Turaev, D., On the Lorenz Attractor in the Shimuizu-Morioka Model, submitted to Nonlinearity.
    • Nonlinearity
    • Tigan, G.1    Turaev, D.2
  • 28
    • 17644427641 scopus 로고    scopus 로고
    • On Dynamical Properties of Diffeomorphisms with Homoclinic Tangencies
    • Gonchenko, S.V., Shilnikov, L.P., and Turaev, D.V., On Dynamical Properties of Diffeomorphisms with Homoclinic Tangencies, J. Math. Sci., 2005, vol. 126, pp. 1317-1343.
    • (2005) J. Math. Sci. , vol.126 , pp. 1317-1343
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3
  • 30
    • 17644417180 scopus 로고    scopus 로고
    • Dynamics and Moduli of Ω-Conjugacy of 4D-Diffeomorphisms with a Structurally Unstable Homoclinic Orbit to a Saddle-Focus Fixed Point
    • Gonchenko, S. V., Dynamics and Moduli of Ω-Conjugacy of 4D-Diffeomorphisms with a Structurally Unstable Homoclinic Orbit to a Saddle-Focus Fixed Point, Amer. Math. Soc. Transl. Ser. 2, 2000, vol. 200, pp. 107-134.
    • (2000) Amer. Math. Soc. Transl. Ser. 2 , vol.200 , pp. 107-134
    • Gonchenko, S.V.1
  • 31
    • 0011277539 scopus 로고
    • On the Existence of Newhouse Regions Near Systems with Non-Rough Poincaré Homoclinic Curve (Multidimensional Case)
    • Gonchenko, S. V., Shilnikov, L.P., and Turaev, D. V., On the Existence of Newhouse Regions Near Systems with Non-Rough Poincaré Homoclinic Curve (Multidimensional Case), Russian Acad. Sci. Dokl. Math., 1993, vol. 47, no. 2, pp. 268-283.
    • (1993) Russian Acad. Sci. Dokl. Math. , vol.47 , Issue.2 , pp. 268-283
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3
  • 32
    • 0002058632 scopus 로고    scopus 로고
    • On Newhouse Regions of Two-Dimensional Diffeomorphisms Close to a Diffeomorphism with a Nontransversal Heteroclinic Cycle
    • Gonchenko, S. V., Shilnikov, L.P., and Turaev, D. V., On Newhouse Regions of Two-Dimensional Diffeomorphisms Close to a Diffeomorphism with a Nontransversal Heteroclinic Cycle, Proc. Steklov Inst. Math., 1997, vol. 216, pp. 70-118.
    • (1997) Proc. Steklov Inst. Math. , vol.216 , pp. 70-118
    • Gonchenko, S.V.1    Shilnikov, L.P.2    Turaev, D.V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.